The admission fee at an amusement park is $1.50 for children and $4 for adults. On a certain day, 274 people entered the park, and the admission fees collected totaled 836.00 dollars. How many adults were admitted?
a. 209
b.170
c.104

Answer:

Let x be the number of free throws Jason made, and y be the number of two point shots he made.

The system of equations will be

x+ 2y = 20x+2y=20

x + y = 13x+y=13

Solving these using elimination method we get,

x + 2y = 20x+2y=20

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

y = 7y=7

x = 6⇒x=6

The number of free throws Jason made are 6, and the number of two point shots he made are 7.

The values of the two original numbers are 7 and 9.

Two numbers when multiplied equal 63 if one number is x and the other number is greater than x by 2.

As per the given phrase, the information given in equation form is as

x × (x + 2) = 63

It expresses as a quadratic equation:

x² + 2x - 63 = 0

Solve the quadratic equation to find possible values of x

x² + 9x - 7x - 63 = 0

x(x + 9) - 7(x + 9) = 0

(x + 9)(x - 7) = 0

(x + 9) = 0 and (x - 7) = 0

x = -9 and x = 7

Since we were told that the two numbers are positive numbers so take x = 7.

Thus, the values of the two original numbers are 7 and 9.

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Answer:

27x^6y^12

Step-by-step explanation:

3^3×x^2(3)×y^4(3)

=27^6y^12

The value of the piecewise function h(x) at x = 2 is (b) -1

From the question, we have the following parameters that can be used in our computation:

Part 1:

h(x) = x cubed for x less than negative 3

Part 2:

h(x) = 2 times x squared minus 9 for negative 3 is less than or equal to x which is less than 4,

Part 3

h(x) = 5 times x plus 4, for x greater than or equal to 4

When the above statements are represented properly, we have the following equations

Part 1: h(x) = x³ for x < -3

Part 2: h(x) = 2x² - 9 for -3 ≤ x < 4

Part 3: h(x) = 5x + 4, for x ≥ 4

To calculate the function h(2), we use the domain -3 ≤ x < 4

So, we have the following function

h(x) = 2x² - 9

Substitute the known values in the above equation, so, we have the following representation

h(2) = 2(2)² - 9

Evaluate the expression

h(2) = -1

Hence, the value is (b) -1

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Complete question

The piecewise function h(x) is shown on the graph.

the function is defined by part 1, which is x cubed for x less than negative 3, part 2, which is 2 times x squared minus 9 for negative 3 is less than or equal to x which is less than 4, and part 3 which is 5 times x plus 4, for x greater than or equal to 4

What is the value of h(2)?

Sasha's balance after 12 years, if she makes no other deposits or withdrawals would be $ 4, 598. 07

Sasha's balance after 12 years will be the future value of her savings after 12 years at a rate of 2. 3% per year.

This future value can be found by the formula :

Amount after 12 years = Amount deposited by Sasha x ( 1 + annual compound interest ) ^ number of years

= 3, 500 x ( 1 + 2 .3 % ) ¹²

= 3, 500 x 1.3137344983996021269289886802331

= $ 4, 598. 07

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The equation to express the total cost, c, to use the Internet at the coffeehouse for t hours is c = rt.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

In this case, the coffeehouse charges a flat rate, r, for each hour a customer wants to use the Internet. An equation to express the total cost, c, to use the Internet at the coffeehouse for t hours.

The equation will be:

c = r(t)

c = rt

where c = cost

t = number of hours

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The expressions that are equivalent to [tex]\frac{10}{9} + \frac{2}{9}m - \frac{4}{9}n[/tex] are [tex]\frac{2}{9}(5 + m -2n)[/tex] and [tex]-\frac{2}{9}( 2n -m -5)[/tex].

Algebraic fractions are fractions using a variable in the numerator or denominator, such as . Because division by 0 is impossible, variables in the denominator have certain restrictions. The denominator can never equal 0.

    [tex]\frac{10}{9} + \frac{2}{9}m - \frac{4}{9}n[/tex] in this algebraic fraction 2/9 is common to all so factoring that out we have

2/9 x 5 + 2/9 x m - 2/9 x 2n so we factor out 2/9

2/9( 5 + m -2n)

This can also be written by multiplying 2/9( 5 + m -2n) by -1 so that it 5becomes

- 2/9(2n -5 - m)

In conclusion the expressions 2/9( 5 + m -2n) and - 2/9(2n -5 - m) are equivalent to [tex]\frac{10}{9} + \frac{2}{9}m - \frac{4}{9}n[/tex]

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Deshaun must save the amount of $275 each month to have enough for the first-year cost.

As per the given question, we have

The first-year cost of college = $25,600

The gift cost = $2500

The amount left to pay will be:

⇒ first-year cost - gift cost

⇒25,600 - 2,500 = 23100

The months left till college = 7 × 12 = 84

So, he would have to save per month :

⇒ 23,100/84

Apply the division operation, and we get

⇒ 275

Thus, he must save the amount of $275 each month to have enough for the first-year cost.

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Answer:

I can't answer unit I know what lines you're talking about, can you insert an image or graph of the questions?

Step-by-step explanation:

The Onion publishes a satirical, comedic story making fun of President Trump. Nothing in the story is remotely true

False information is presented as fake news. This is bogus news since the onion published a satirical fictional report about President Trumb. GSU fabricates false, deceptive information, often known as false news. False news is not defined as news that has factual inaccuracies.

GSU intentionally produces and disseminates a phony but plausible-looking news item touting the excellent parking situation on campus in an effort to boost applicants.

The term "fake news" describes news sources that pose as authentic while actually being false. It frequently aims to make money from advertising or to harm someone's or an organisation's reputation.

By purposefully fabricating and spreading a bogus but plausible-looking news article claiming how excellent the parking situation is on campus, GSU hopes to increase the number of applications. Which is false information that will cause people to come forward with job applications.

The Onion publishes a satirical, comedic story making fun of President Trump. Nothing in the story is remotely true

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The system of linear equation have an ordered triple of (x, y, z) are (-3, 1, -8)

To evaluate an algebraic expression, you have to substitute a number for each variable and perform the arithmetic operations.

In the question given, we have a system of linear equations where the value of x and y are given.

-5x - 4y + 2z = -5 ...eq(i)

-4x + 2y + 3z = 38 ...eq(ii)

2z + 3y + 4z = -35 ...eq(ii)

Since we have the value two variables (x, y) which are (-3, 1), we can substitute it in any of the equation to find the value of z.

Taking eq(i)

-5x - 4y + 2z = -5

-5(-3) - 4(1) + 2z = -5

15 - 4 + 2z = -5

11 + 2z = -5

2z = -5 - 11

2z = - 16

z = -8

The ordered triple are (-3, 1, -8)

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Answer:

-0.3

Step-by-step explanation:

just sum -0.66x and 0.36x

Answer: -21

Step-by-step explanation:

To begin, we can combine like terms, -0.66 and 0.36 are coefficients with the same variable.

This gives us -0.66x+0.36x= -0.30x, and the equation becomes -0.30x=6.3.

Next, we can simply solve for x by dividing 6.3 by -0.30, and that gives us x=-21.

The equation of the line passing through (7, -2) and (5, 3) is 5x + 2y - 31 = 0.

What is two point equation form?

The equation of the line passing through two points is

(y - y₁) / (y₂ - y₁) = (x - x₁) / (x₂ - x₁)

Here, (x₁,y₁) ∈ (7, -2)

(x₂, y₂) ∈ (5, 3).

y - (-2) / 3 -(-2) = x - 7/ 5 - 7

(y + 2) / 5 = x-7 / -2

-2y - 4 = 5x - 35

5x + 2y - 31 = 0

Hence, the equation of the line passing through (7, -2) and (5, 3) is 5x + 2y - 31 = 0.

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The triangles ΔSTU and ΔRQV are congruent triangles

Two triangles are congruent if the three sides of one triangle are congruent to the three sides of the other triangle.

The parameters from the diagram includes;

Side [tex]\overline{TU}[/tex] in triangle ΔSTU is congruent to side [tex]\overline{QV}[/tex] in triangle ΔRQV

Segment [tex]\overline{UV}[/tex] is congruent to segment [tex]\overline{RS}[/tex]

[tex]\overline{UV}[/tex] ≅ [tex]\overline{RS}[/tex]

[tex]\overline{UV}[/tex] = [tex]\overline{RS}[/tex] By definition of congruency

Side [tex]\overline{ST}[/tex] in triangle ΔSTU is congruent to side [tex]\overline{QR}[/tex] in triangle ΔRQV

Segment [tex]\overline{RU}[/tex] is congruent to segment [tex]\overline{UR}[/tex], by reflexive property

[tex]\overline{RV}[/tex] = [tex]\overline{RU}[/tex] + [tex]\overline{UV}[/tex] by segment addition postulate

Similarly, [tex]\overline{SU}[/tex] = [tex]\overline{RU}[/tex] + [tex]\overline{RS}[/tex]

Therefore; [tex]\overline{SU}[/tex] = [tex]\overline{RU}[/tex] + [tex]\overline{UV}[/tex] (by substitution property)

[tex]\overline{RV}[/tex] = [tex]\overline{SU}[/tex] by substitution property

[tex]\overline{RV}[/tex] ≅ [tex]\overline{SU}[/tex] by definition of congruency

The three sides of the triangle ΔSTU are congruent to the three sides of the triangle ΔRQV, therefore;

The triangles ΔSTU and ΔRQV are congruent by Side-Side-Side, SSS, congruency postulate

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The current value of his mortgage must be no higher than $126,360 for him to request termination of his PMI policy.

What is mortgage value?

The appraised value of the property used to determine the mortgage value is determined by a reputable firm. It might not match the purchase-sale value. The mortgage value, which serves as the Bank's guarantee, is the benchmark used in the mortgage application and arrangement process.

Given:

Brett bought a house five years ago for $150,000.

At that time he borrowed $140,000 from his bank.

The house is now worth $162,000.

Once his equity has increased to 22% of the current market value he can request that PMI be canceled.

He may request termination of request when his mortgage balance reaches

162,000(1 - 0.22) = 162,000(0.78) = 126,360.

Hence,  the current value of his mortgage must be no higher than $126,360 for him to request termination of his PMI policy.

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Answer:

2((2x+2)+3x)=124 units

Step-by-step explanation:

We know that the formula for perimeter is 2(b+h) and since we know this, we just substitute the values for this and solve.

Next step is to Mark off your new arc with this new width by positioning the compass point on the reference line where the previous arc crossed it.

Steps to be followed while measuring an exact angle using compass and straight edge are:

Swing the arc so that the pencil crosses BOTH rays (sides) of the angle. Holding the compass point at the starting point (dot) on the reference line, swing an arc that will cross the reference line and rise above the reference line without adjusting the compass's size. Return to the supplied angle ABC and determine the span (width) of the arc between the points at which it crosses one side of the angle and the other. Mark off your new arc with this new width by positioning the compass point on the reference line where the previous arc crossed it. Join this new intersection point to the reference line's starting point. Mark the duplicate.

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the center of the circle is at (5, 1) and the radius is approximately 5.48 units.

Why it is and what is perimeter of a circle?

The standard equation of a circle with center (a,b) and radius r is:

(x - a)²2 + (y - b)²2 = r²2

Comparing this equation to the given equation, we can see that the center of the circle is (5, 1) and the radius is the square root of 30. Therefore, the center of the circle is at (5, 1) and the radius is approximately 5.48 units.

The perimeter of a circle is also known as its circumference, and it can be calculated using the formula:

C = 2πr

where C is the circumference, r is the radius of the circle, and π (pi) is a mathematical constant approximately equal to 3.14159.

Alternatively, you can also use the formula:

C = πd

where d is the diameter of the circle.

So if you know the radius or diameter of a circle, you can use either of these formulas to calculate its circumference (perimeter).

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Answer:

cosU = [tex]\frac{3}{4}[/tex]

Step-by-step explanation:

cosU = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{TU}{ST}[/tex] = [tex]\frac{6}{8}[/tex] = [tex]\frac{3}{4}[/tex]

The z values are-

Obtain the  z values from the t-distribution table for 0.86 and  0.78 confidence interval.

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The equation of a line that represents the table is y = 6x - 5.

We know lines have various types of equations, the general type is

Ax + By + c = 0, and the equation of a line in slope-intercept form is

y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

To obtain the linear equation first we need slope(m) = (y₂ - y₁)/(x₂ - x₁)

= (1 + 11)/(1 + 1) = 12/2 = 6.

Now, we'll take any one of these coordinate points and construct an equation in slope-intercept form,

- 11 = 6(-1) + b.

- 11 = - 6 + b.

b = - 5.

∴ y = 6x - 5 is our equation.

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To find the percent of change, we need to calculate the difference between the original price and the new price, and then divide this difference by the original price and multiply by 100%.

The difference between the original price of $20 and the new price of $55 is $55 - $20 = $35.

The percent of change is: ($35/$20) * 100% = 1.75 * 100% = 175%

Since the new price is higher than the original price, this is an increase. Therefore, the percent of change is a 175% increase. The correct answer is therefore

O 175% increase.

Answer:

y = -3x + 10

Step-by-step explanation:

slope of perpendicular line = -3

y-1 = -3(x-3)

y-1 = -3x + 9

y = -3x + 9 + 1

y = -3x + 10

The time taken by the person to cover 260 miles will be 3 hours and 15 minutes.

Speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance. Speed is the ratio of the distance travelled by time. The unit of speed in miles per hour.

Given that a person to drive 260 miles on a highway if she merges onto a highway at 7 p.m. and drives nonstop with her cruise control set at 80 mph.

The amount of time taken by the person to cover the distance of 260 miles with a speed of 80mph is,

Speed = Distance / Time

Time = Distance / Speed

Time = 260 / 80

Time = 3.25 or 3 hours 15 minutes

Therefore, the time taken by the person to cover 260 miles will be 3 hours and 15 minutes.

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Answer:

m1= 35

m2= 65

m3= 29

m4= 115

m5=65

The values of the functions g[f(0)]b) f(-5), f[h(3)], h°f(x) and h⁻¹(x) are 9.5, -2, 16, (4x+22)/x and 6/(x-2) respectively

A function is a relationship between inputs where each input is related to exactly one output

Given:  f(x)= 2x+8, g(x)= 5x-2/4 and h(x)= 2x+6/x

(a) g[f(0)]

Substitute x = 0 into  f(x)= 2x+8 to get f(0)

f(0) = 2(0)+8 =8

g[f(0)] =  g(8)

Substitute x = 8 into g(x)= 5x-2/4 to get g[f(0)]

g[f(0)] =  g(8)

g[f(0)]  = 5x-2/4

g[f(0)]  = 5(8)-2/4 = 9.5

b) f(-5)

Substitute x = -5 into  f(x)= 2x+8 to get f(-5)

 f(x)= 2x+8

f(-5)= 2(-5)+8 = -2

c) f[h(3)]

h(x)= 2x+6/x

h(3) = 2(3)+6/3 = 4

f[h(3)] = f[4]

f[4] = 2(4)+8 = 16

f[h(3)]  = 16

d) h°f(x)

h°f(x)  = h(2x+8)  

Since h(x)= 2x+6/x

h°f(x) = 2(2x+8) +6/x

h°f(x) = 4x+16+6/x = (4x+22)/x

e) h⁻¹(x)

h(x)= 2x+6/x

Let y = 2x+6/x

x = 6/(y-2)

x = h⁻¹(y)

h⁻¹(x) = 6/(x-2)

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The side of square park, whose fencing costed Rs 2880 is 36m.

What is a square?

A quadrilateral with four equal sides is called a square. There are numerous items in our environment that have a square shape. Equal sides and internal angles that are both 90 degrees distinguish each square shape. Let's find out more about a square's characteristics, mathematics, and design.

We know perimeter of a square of side 'a' is 4a

Therefore, the cost of fencing a square park at Rs 20/meter would be equal to

= Rs(20*4a)

= Rs 80a

Given, the cost of fencing = Rs 2880

Thus, 80a = 2880

⇒ a = 2880/80

⇒ a = 36

Thus, the side of square park, whose fencing costed Rs 2880 is 36m

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