At a museum, the admission price for children is $9 and the admission price for adults is $16. The total amount the museum collects in admissions for the day is $4650. The total number of visitors is 330. Let x be the number of children and let y be the number of adults. Which system represents the situation?

Answer:

The mistake is that from Step 1 to Step 2, Jorge did not add 0.25 correctly to both sides.

Step-by-step explanation:

If Marcel has $8.25 and is only playing $0.25 games, then the equation will be given by:  8.25 - 0.25X.

If Floyd has $9.75 and is only playing $0.75 games, then the equation will be given by:  9.75 - 0.75X.

If we want to find the number of games after which Marcel and Floyd will have the same amount of money remaining, we need to solve the system of equations:

Equation: 8.25 - 0.25X = 9.75 - 0.75X

Step 1: -1.50 - 0.25X = - 0.75X

Step 2: -1.50 = - 0.50X

Step 3: x=3

The mistake is that from Step 1 to Step 2, Jorge did not add 0.25 correctly to both sides.

Answer: Option B

From Step 1 to Step 2, Jorge did not add 0.25x correctly to both sides.

Step-by-step explanation:

To solve this problem, let's consider the initial equation that Jorge had.

[tex]8.25-0.25x=9.75-0.75x[/tex]

Subtract 9.75 on both sides of equality

[tex]8.25-9.75-0.25x=9.75-9.75-0.75x[/tex]

[tex]-1.50-0.25x=-0.75x[/tex]

Add 0.25x on both sides of equality

[tex]-1.50-0.25x+0.25x=-0.75x+0.25x[/tex]

[tex]-1.50=-0.50x[/tex]

[tex]x=3[/tex]

You can see then that Jorge's error was adding [tex]-0.75x + 0.25x[/tex]

When this sum is correctly done, the result is [tex]-0.50x[/tex]

The answer is the option B.

Answer:

12 days

Step-by-step explanation:

Sally has  pet snail that fell into a well.

Depth of the well = 16 feet

Snail climbs up 5 feet but each night it slides back down 4 feet.

So the snail climbs up per day = 5 feet - 4 feet = 1 feet.

Number of days snail took to reach at 11 feet = 11 × 1 = 11 feet

Remaining distance to cover by the snail = 16 - 11 = 5 feet

Number of days to cover remaining 5 feet to reach the top of the well = 1 day

Therefore, snail will take 12 days to reach the top of the well.

Final answer:

The snail climbs up 5 feet and slides back 4 feet each day in a 16-foot deep well. With a net gain of 1 foot per day, the snail will escape on the 16th day after reaching the top without sliding back.

Explanation:

Sally's pet snail finds itself in a classic mathematical problem often associated with algebra and arithmetic sequences. The snail is attempting to escape a 16-foot deep well by climbing up 5 feet during the day and sliding back 4 feet each night. To determine how many days it will take for the snail to get out, we need to calculate the net progress made by the snail each day and then examine how this applies on the final day of the snail's ascent.

Each day, the snail makes a net gain of 1 foot (5 feet up during the day minus 4 feet down at night). After 15 days, the snail would have climbed 15 feet during the day. On the 16th day, the snail climbs up 5 feet and reaches the top of the well, coming out without sliding back down since it already reached the goal during daylight. Therefore, it will take the snail a total of 16 days to escape the well.

Units are written in bracelets.

[tex]F=ma \: \{kg\cdot\dfrac{m}{s^2}\}[/tex]

[tex]F=ma \: \{\boxed{\dfrac{kg\cdot m}{s^2}}=N\}[/tex]

Hope this helps.

r3t40

Answer:

Step-by-step explanation:

Force is defined as a function of mass (denoted by m) and acceleration (denoted by a) using this formula F=ma

units for mass m is kg

units for acceleration is metre/sec^2

Hence together we can write unit as

unit for force = [tex]Kg m/sec^2[/tex]

This can also be expressed as newtons

Unit for force = newtons also.

Replace x with the binomial a - 2.

f(a - 2) = [3(a - 2) + 5]/(a- 2)

f(a - 2) = [3a - 6 + 5]/(a - 2)

f(a - 2) = [3a - 1]/(a - 2)

f(a - 2) = (3a - 1)/(a - 2)

Done.

Answer:

D

Step-by-step explanation:

The first and last sequence have a common difference in them. The first having d = 4 and the second having d = 7.

The second and third have a common ratio instead and are geometric sequences. The second has r = 2, and the third having r = (-3)

Answer:

B

Step-by-step explanation:

The common ratio in this case, is something that is going to make the geometric sequence go down. Your will make it go up.

Common ratio = second term / first term

common ration = 125/625 = 25/125 which is obtained by dividing both top and bottom of the fraction by 5.

Its not the best possible answer, but it is the best among those given.

Answer:

1/5

Step-by-step explanation:

Notice that 125 is 1/5 th of 625; 25 is 1/5 th of 125; 5 is 1/5 of 25, and so on.

Thus, the common ratio is 1/5.

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Answer:

The equation is [tex]10x+35 =5x+40[/tex]

Step-by-step explanation:

Let

x --> the charge per hour to ski  

y ---> the total charge for ski

we know that

Bunny Hill Ski Resort

[tex]y=10x+35[/tex]----> equation A

Black Diamond Ski Resort

[tex]y=5x+40[/tex] ----> equation B

equate equation A and equation B

[tex]10x+35=5x+40[/tex]

solve for x

[tex]10x-5x=40-35[/tex]

[tex]5x=5[/tex]

[tex]x=1\ hour[/tex]

Find the value of y

[tex]y=10(1)+35=\$45[/tex]

therefore

At point (1,45) the cost of both ski resort is the same

Answer:

Option B is correct.

Step-by-step explanation:

4x+3y-z= -6     eq(1)

6x-y+3z= 12     eq(2)

8x+2y+4z=6    eq(3)

We need to solve these equations and find the value of x, y and z.

Multiply equation 2 with 3 and then add equation 1 and 2

18x -3y +9z = 36

4x +3y -z = -6

_____________

22x + 8z = 30    eq(3)

Multiply equation 2 with 2 and add with equation 3

12x -2y + 6z = 24

8x +2y +4z = 6

____________

20x + 10 z = 30  eq(4)

Multiply equation 3 with 10 and equation 4 with 8 and then subtract

220x + 80z = 300

160x + 80z = 240

-        -            -

_________________

60x = 60

x= 60/60

x= 1

Putting value of x in equation 3

22x + 8z = 30

22(1) + 8z = 30

8z = 30 - 22

8z = 8

z = 8/8

z=1

Putting value of x and z in equation 1

4(1)+3y-(1)=-6

4 + 3y -1 = -6

3 + 3y = -6

3y = -6 -3

3y = -9

y = -3

so, Option B x=1, y=3 and z=1 is correct

Answer:

b

Step-by-step explanation:

Answer:

23rd hours

Step-by-step explanation:

This is problem based on arithmetic progression in which our first term is 45 , and the common difference is -2

we have to find the n when the nth term is 2.

The formula for nth term of an AP is

[tex]a_{n}=a+(n-1)d[/tex]

replacing the  values in the formula

[tex]a_{n}=a+(n-1)d\\2=45+(n-1)(-2)\\2=45-2(n-1)\\-43=-2(n-1)\\21.5 = n-1\\n=22.5\\[/tex]

hence at 22.5 hours it will reach 2F or we can say that after 23 hours the temperature will be below 2F

Answer:

40°

Step-by-step explanation:

In any circle the following ratios are equal

let x be the measure of the central angle, then

[tex]\frac{arc}{circumference}[/tex] = [tex]\frac{x}{360}[/tex]

circumference = 2πr = 2π × 18 = 36π, so

[tex]\frac{4\pi }{36\pi }[/tex] = [tex]\frac{x}{360}[/tex], that is

[tex]\frac{1}{9}[/tex] = [tex]\frac{x}{360}[/tex] ( cross- multiply )

9x = 360 ( divide both sides by 9 )

x = 40

Hence central angle = 40°

Answer with explanation:

1.→→→ 3x-5y=15------(1)

6 x-10 y=30----(2)

Line 2 =2 * Line 1

These two lines are coincident.

Dependent

2.→→→ -2 x+4 y=-6-------(1)

Dividing both sides by , 2 we get

-x+2y= -3-----------------(1)

x+6 y=3------------(2)

These two are distinct lines ,it means they have a common point of intersection.

Consistent, and Independent

3.→→→

x-4y = -12-----------------(1)

3x-12 y= -9--------------(2)

Equation (2)=3 * Equation (1)

These two lines are coincident.

Dependent

4.→→→

3 x+y=3------(1)

6x+2y=-4------(2)

Dividing both sides by ,2 we get

3 x+y= -2

Both lines have distinct y intercepts that is ,3 and -2,but coefficient of x and y are equal. So, they are parallel lines.

Inconsistent

1.→→→ 3x-5y=15------(1)

6 x-10 y=30----(2)

Line 2 =2 * Line 1

These two lines are coincident.

Dependent

2.→→→ -2 x+4 y=-6-------(1)

Dividing both sides by , 2 we get

-x+2y= -3-----------------(1)

x+6 y=3------------(2)

These two are distinct lines ,it means they have a common point of intersection.

Consistent, and Independent

3.→→→

x-4y = -12-----------------(1)

3x-12 y= -9--------------(2)

Equation (2)=3 * Equation (1)

These two lines are coincident.

Dependent

4.→→→

3 x+y=3------(1)

6x+2y=-4------(2)

Dividing both sides by ,2 we get

3 x+y= -2

Both lines have distinct y intercepts that is ,3 and -2,but coefficient of x and y are equal. So, they are parallel lines.

Answer:

-3

Step-by-step explanation:

Answer:

The slope of the line is [tex]m=-3[/tex]

Step-by-step explanation:

For a linear equation of the form

[tex]y = mx + b[/tex]

the slope of the line is the constant m

in this case we have the equation

[tex]y + 1 = -3x[/tex]

Solving for y we have:

[tex]y = -3x -1[/tex]

Then [tex]m = -3[/tex]

The slope of the line is -3

Answer:

He needs 3.75 lbs of sugar and 1.25 lbs of water.

Step-by-step explanation:

Let x lbs be the amount of sugar in the syrup. Then 5-x lbs is the amount of water in this syrup.

Note

5 lbs - 100%

x lbs - 75%

Write a proportion:

[tex]\dfrac{5}{x}=\dfrac{100}{75}[/tex]

Cross multiply:

[tex]100x=5\cdot 75\\ \\100x=375\\ \\x=\dfrac{375}{100}=3.75[/tex]

So, he needs 3.75 lbs of sugar and 5 - 3.75 = 1.25 lbs of water.

Answer:

3.75 lbs of sugar and 1.25 lbs of water

Step-by-step explanation:

:)

Answer:

The fourth graph shows and exponential growth function.

Step-by-step explanation:

The last graph shows the value increasing by a large amount.

An exponential function can represent growth or decay.

The graph represents an exponential growth function is graph (d)

An exponential function is represented as:

[tex]y = ab^x[/tex]

Where:

b represents the growth or decay rate of the function

When the value of b is greater than 1, then the exponential function represents growth

From the diagrams, only the last graph represent an exponential growth function.

Hence, the graph represents an exponential growth function is graph (d)

Read more about exponential functions at:

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Step-by-step explanation:

The volume of a prism is:

V = AH

where A is the area of the base and H is the height.

The base is a triangle, so the area is:

A = 1/2 b h

We know that b = 3.  To find h, we can split the triangle in half.  Then we can either use Pythagorean theorem to find h, or properties of a 30-60-90 triangle.

The short leg is 3/2, so the height is 3/2 √3.

A = 1/2 (3) (3/2 √3)

A = 9/4 √3

Therefore:

V = (9/4 √3) (6)

V = 27/2 √3

Answer:

C

Step-by-step explanation:

Since the angles at the centre subtended by the congruent arcs WX and YZ

Then ∠YOZ = ∠WOX = 103° → C

The measure of the angle YOZ is b°.  Option c is correct.

In a circle arc WX and YZ are congruent. Than angle YOZ is to be determine.

Arc is defined as the circular curve or part of circle. Arc = angle * radius.

Here, arc WX = arc YZ
If arc is equal in a circle than angle sub tainted by this arc to center are also equal.
angle YOZ = angle WOX = 103°

Thus, the measure of the angle YOZ is 103°.

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Answer:

5

Step-by-step explanation:

1. Find the Mean

(2+8+10+16)/4=9

2.For each number, subtract the Mean and square the result.

(2-9)^2=49

(8-9)^2=1

(10-9)^2=1

(16-9)^2=49

3. Find the Mean of those squared differences.

(49+1+1+49)/4=25

4.Take the square root of that and this is what you want.

square root of 25 = 5

If the value of the mean is 9. Then the mean absolute deviation will be 4.

It is the average distance between each data point and the mean.

The MAD is given as

[tex]\rm MAD = \dfrac{\Sigma _{i = 1}^n|x_i - \mu|}{n}[/tex]

The data set is given below.

2,8,10,16

Then the mean will be

μ = (2 + 8 + 10 + 16) / 4

μ = 36 / 4

μ = 9

Then the mean absolute deviation will be

MAD = (|2 - 9| + |8 - 9| + |10 - 9| + |16 - 9|) / 4

MAD = (7 + 1 + 1 + 7) / 4

MAD = 16 / 4

MAD = 4

More about the mean absolute deviation link is given below.

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Answer:

(x−8)2+C−64(x-8)2+C-64

Answer:

It will be any graphs that show a parallel line relationship.

Explanation:

Any graph that shows parallel lines will always be no solution.

Answer:

It have to be a graph that shows functions that doesn't have points in common. The figure show some examples.

For this case we must find the product of the following expression:

[tex]\sqrt [3] {5} * \sqrt {2}[/tex]

By definition of properties of powers and roots we have:

[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]

We rewrite the expression using the lowest common index of 6, then:

[tex]5 ^ {\frac {1} {3}} * 2 ^ {\frac {1} {2}} =[/tex]

We rewrite the terms in an equivalent way:

[tex]5 ^ {\frac {2} {6}} * 2 ^ {\frac {3} {6}} =[/tex]

We rewrite the expression using the property mentioned:

[tex]\sqrt [6] {5 ^ 2} * \sqrt [6] {2 ^ 3} =[/tex]

We combine using the product rule for radicals:

[tex]\sqrt [n] {a} * \sqrt [n] {b} = \sqrt [n] {ab}[/tex]

So:

[tex]\sqrt [6] {5 ^ 2 * 2 ^ 3} =\\\sqrt [6] {25 * 8} =\\\sqrt[6]{200}[/tex]

ANswer:

Option b

Answer:

1. 50 cm

2. 550 mm

3. 5000 mm

4. 5000 cm

5. 5000 m

Step-by-step explanation:

We can convert all the measures in same unit to arrange them one by one.

5000 cm:

As there are 10 millimeters in 1 cm,

5000 cm = 5000*10mm

=> 50000 mm

5000 meters:

As there are 100 cms in one meter

5000 m = 5000*100 cm

=> 500000 cm

Now to convert in millimeter

500000*10= 5000000 mm

50 cm:

50*10 = 500 mm

Then there is 550 mm and 5000 mm

So, the order from least to greatest is:

1. 500 mm which is equivalent of 50 cm

2. 550 mm

3. 5000 mm

4. 50000 mm which was equivalent of 5000 cm

5. 5000000 mm which was equivalent of 5000 m ..

Final answer:

To compare the given measurements, we converted each one to millimeters (mm) using a conversion table, then arranged them in ascending order: 50 cm (500 mm), 550 mm, 5,000 mm, 5,000 cm (50,000 mm), and 5,000 m (50,000,000 mm).

Explanation:

To determine which of the given measures is the smallest and which is the largest, we need to convert each measure to the same unit for comparison. Using the ratio conversion table, we will convert all measures to millimeters (mm).

Now we arrange the measures in order from least to greatest:

Answer:

y=3x-7

Step-by-step explanation:

Two points on the line are (3,2) and (4,5) using the slope equation, 5-2/4-3=3/1

y-2=3(x-3)

(2+) y-2=3x-9(+2)

y=3x-7

[tex]\bf (\stackrel{x_1}{-2}~,~\stackrel{y_1}{1})\qquad ~\hspace{10em}slope = m\implies 4 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-1=4[x-(-2)]\implies y-1=4(x+2) \\\\\\ y-1 = 4x+8\implies y=4x+9[/tex]

Approximately 18.42% of the beef production annually worldwide comes from the U.S.

In the U.S., 12.0 million metric tons of beef are produced annually, while worldwide beef production is 65.1 million metric tons.

To find the percentage of beef produced in the U.S. compared to worldwide production, you can divide the U.S. beef production by the worldwide beef production and multiply by 100.

Percentage = ( U.S. beef production / Worldwide beef production ) x 100 = ( 12.0 million / 65.1 million ) x 100 = 18.42%.

Therefore, approximately 18.42% of the beef produced annually in the world is from the U.S.

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Answer:(x^2+y^2)^2=(x^2+y^2)(x^2+y^2)

Step-by-step explanation:

We can rewrite left side into right side form

(x^2+y^2)^2=(x^2+y^2)(x^2+y^2)

we can expand it

(x^2+y^2)^2=x^4+x^2y^2+x^2y^2+y^4

(x^2+y^2)^2=x^4+y^4+2x^2y^2

we can add and subtract 2x^2y^2

(x^2+y^2)^2=x^4+y^4+2x^2y^2+2x^2y^2-2x^2y^2

(x^2+y^2)^2=x^4-2x^2y^2+y^4+2x^2y^2+2x^2y^2

(x^2+y^2)^2=x^4-2x^2y^2+y^4+4x^2y^2

(x^2+y^2)^2=x^4-2x^2y^2+y^4+(2xy)^2

(x^2+y^2)^2=(x^2-y^2)^2+(2xy)^2

The Pythagorean triple generator typically involves an algebraic formula where variables m and n are used to generate the sides of a right triangle such that a^2 + b^2 = c^2, with a common formula being a = m^2 - n^2, b = 2mn, and c = m^2 + n^2 for positive integers m and n.

The form of the Pythagorean triple generator refers to a set of algebraic formulas that produce Pythagorean triples, which are sets of three positive integers (a, b, c) that satisfy the condition of the Pythagorean theorem (a^2 + b^2 = c^2) for a right triangle.

One well-known formula to generate these triples is given by:

where m and n are positive integers with m > n. This formula will produce a Pythagorean triple as long as m and n are coprime and not both odd. It's important to note that not all Pythagorean triples can be generated by this formula, but it is a very common method of finding such triples.

Answer:

1,110 is a cluster because it’s a very large number for 52 degrees and 189 is because it’s a very large number for 16 degrees.

Step-by-step explanation: I'm happy to help...

The equation [tex]2x^{3} -10x^{2} -12x[/tex] has 2 and x in common. This means you can factor both the 2 and x out of the equation like so...

2x([tex]x^{2} -5x-6[/tex])

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

2x(x - 6)(x + 1)

Step-by-step explanation:

Given

2x³ - 10x² - 12x ← factor out 2x from each term

= 2x(x² - 5x - 6)

To factor the quadratic

Consider the factors of the constant term (- 6) which sum to give the coefficient of the x- term (- 5)

The factors are - 6 and + 1, since

- 6 × 1 = - 6 and - 6 + 1 = - 5, thus

x² - 5x - 6 = (x - 6)(x + 1) and

2x³ - 10x² - 12x = 2x(x - 6)(x + 1) ← in factored form

Answer: 45°

Step-by-step explanation:

Because AB and CD are parallel, angle x must be congruent with its corresponding angle.

Step-by-step explanation:

Use Pythagorean theorem:

c² = a² + b²

Here, c = 42 and a = 31.

42² = 31² + b²

b = √803

b ≈ 28.3