A group of friends wants to go to the amusement park. They have no more than $160 to spend on parking and admission. Parking is $10.50, and tickets cost $32.50 per person, including tax. Write and solve an inequality which can be used to determine x, the number of people who can go to the amusement park.​

For the rectangle given, considering its diagonal properties, the value of x=4, while the angle VUR=36°

To answer this question, let us recall the following:

Hence;

the lengths RV and SV are

so, 3x+8=6x-4

6x-3x=8+4 [collecting like terms]

3x=12

when we divide both sides of the equation by 3, we have the value of x=4.

the angles VRS and VRU are complementary

so, 54°+VRU = 90°

VRU = 90°-54°

VRU = 36°

The triangle RUV is an Isosceles

so, angles VRU and VUR are equal, therefore angle VUR = 36°.

We can reduce from our workings that the value of x = 4 and the angle VUR is 36°.

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The operations that would increase the value of a given number include the following:

A. Multiply the number by 10.

D. Divide the number by 0.1.

The operations that would decrease the value of a given number include the following:

B. Multiply the number by 0.1.

C. Divide the number by 10.

Multiplication is a mathematical operation which can be used to increase the value of a given number, especially by multiplying the number by a value that is greater than 1. Similarly, the value of a given number can also be increased by dividing it by a number that is lesser than 1 such as 0.1

Multiplication is a mathematical operation which can be used to decrease the value of a given number, especially by multiplying the number by a value that is lesser than 1. Similarly, the value of a given number can also be decreased by dividing it by a number that is greater than 1 such as 10.

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Answer:

12

Step-by-step explanation:

Equation:

[tex]9 /\frac{3}{4}[/tex] [tex]=x[/tex]

[tex]12=x[/tex]

Check!

[tex]12(\frac{3}{4} )=9[/tex]

Therefore, the greatest number of file boxes that can be stacked is 12.

Answer:

see below

Step-by-step explanation:

sum of angles in right triangle is 180

90 + 50 = 140

b = 180 - 140 = 40 deg

find c

cos(50) = 20/ c

c = 20/cos(50) = 31.1

find a

tan(40) = 20/a

a = 20/tan(40) = 23.8

Answer:

Step-by-step explanation:

a. From 4 to 7 is 3 units. 7-10 is another 3 units and so on. The constant 3 units is the common difference.

The formula for a arithmetic sequence is

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

Where d is the common difference and a_1 is the first term.

[tex]a_{1}=4[/tex] and [tex]d=3[/tex]. Thus the equation of the nth term is

[tex]a_{n}=4+3(n-1)[/tex]

A) The slope represents the probability of winning for each rank.

B) The y-intercept means the probability of winning for an unranked school.

C) The probability of winning for a school ranked number 4 is; 78%

The formula representing the general form of an equation in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

A) From the given graph, we see that the y-axis represents the probability of winning for each rank while the x-axis represents the ranks of the schools. Thus;

Slope unit = Probability of winning/Rank

B) The y-intercept is the point at which the graph crosses the y-axis. In this case, it means no ranked school and that is the probability of winning for an unranked school.

C) The linear equation is given by the formula;

y = -6.4x + 103.8

Thus, for a rank of 4, we have;

y = -6.4(4) + 103.8

y = 78.2 ≈ 78%

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The difference of population in these two cities are 85900- 3200

= 82,700

Subtract the largest number from the lowest number to determine the difference between two integers. The difference between the two numbers is the product of this sum. As a result, there are 55 between the numbers 45 and 100.

Given: Population of city A= 8.59 x 10^4

and population of city B = 3.2 x 10^3

This can also be written as :

Population of city A= 85,900

and population of city B = 3200

Thus the difference of population in these two cities are 85900- 3200

= 82,700

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The formula Arya stark will use to find the 95% confidence interval is normal approximation of the distribution.

For the given question, the data is-

The formula for finding the 95% confidence interval is normal approximation of the distribution.

z = (x - μ)/s

Where, s = σ/√n

The corresponding value of z for 96% is taken from the z score table.

Thus,  formula Arya stark will use to find the 95% confidence interval is normal approximation of the distribution.

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The x-intercept is (27,0). The time it takes to reach the bus stop

We first find the equation between time and distance as a linear function by finding the slope and y-intercept from the table values.

If we write the Time as x-values and Distance as y-values, we get the points,

(0,45), (3,40), (6,35), (9,30), (12,25)

We can find the slope from these points considering two points (0,45) and (3,40)

Slope = 45-40/0-3 = -5/3

The y-intercept of the function is the value of f(x) at x = 0.

Here, from the table, when x = 0, y = 45.

So y-intercept = 45

Then the equation of distance in terms of time is,

y = -(5/3)x+45

The x-intercept is the x-value when y = 0.

So when y = 0,

0 = -(5/3)x+45

⇒ (5/3)x=45

⇒ x = 45x 3/5

⇒ x = 27

Therefore, x-intercept = (27,0).

It is the time (in minutes) when distance = 0 meters.

So x-intercept is the time it takes to reach the bus stop.

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Answer:

B)  (27,0); the time it takes to reach the bus stop

To find the probability that the mean IQ score of people in the sample is less than 98, first we need to convert the value into z-score by using the formula:

Then, when x=98:

By checking in a standard normal table z=-0.1333 has a p-value=0.4471.

Then the probability is 0.4471 that also can be expressed as 44.71%

Answer:

1 ≤ y ≤ 4

Step-by-step explanation:

Range is all possible y values

a point is written as (x, y)

The line starts at point (0, 1) and ends at (3, 4)

so the range of the y values is 1 to 4

The system of equations has two solutions, these are:

(-0.89, 2.33) and (1.4, 9.2)

Here we have the following system of equations:

y = 3x + 5

y = 4x² + x

We can see that y is already isolated in both equations, so we can write the equation:

3x + 5 = y = 4x² + x

3x + 5 = 4x² + x

now we can solve this for x, this is just a quadratic equation:

3x + 5 - 4x² - x = 0

-4x² + 2x + 5 = 0

Using the quadratic formula, we can see that the two solutions are:

[tex]x = \frac{-2 \pm \sqrt{2^2 - 4*(-4)*5} }{2*-4} \\\\x = \frac{-2 \pm 9.17}{-8}[/tex]

So the solutions are:

x = (-2 +9.17)/-8 = -0.89

x = (-2 - 9.17)/-8 = 1.4

Evaluating the linear equation in these values, we get:

y = 3*(-0.89) +5 = 2.33

y = 3*(1.4) + 5 = 9.2

So the solutions of the system are:

(-0.89, 2.33) and (1.4, 9.2)

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Answer:

76.25

Step-by-step explanation:

61:48 = x:60

48x=3660

3660/48 = 76.25

So the answer is 76.25 miles are left.

Step-by-step explanation:

a parallel line must have the same slope (otherwise it cannot be parallel).

a slope-intercept form looks like

y = ax + b

"a" (the factor of x) is always the slope, "b" is the y-intercept (the y-value when x = 0).

so, we know from y = -3x + 5 that the slope of the new line is also -3.

to get b we use the coordinates of the given point :

-5 = -3×-8 + b = 24 + b

-29 = b

that means the line equation is

y = -3x - 29

The single inequality y > |x + 2| is equivalent to:

4. y > x + 2

y < –x – 2

It should be noted that an inequality is simply used to show the relationship between the expressions that aren't equal.

The non-negative value of a real number x, regardless of its sign, is its absolute value or modulus | x |. For instance, 5 has an absolute value of 5, and 5 has a value of 5. One way to think about a number's absolute value is as its distance from zero on the real number line.

It should be noted that based on the information, the inequality is:

y > |x + 2|. This is the positive part of the modulus.

This is the same as y < –x – 2 when the signs are changed. This is the negative part of the modulus.

In conclusion, the correct option is 4.

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The 64 fluid ounces of water, as suggested by Kamryn's doctor to drink everyday, will be equal to 1920 millilitres.

Writing the equation as per the relation between millilitres and fluid ounces -

1 fluid ounce = 30 millilitres

Now, we will perform multiplication to find the number of milliliters in 64 fluid ounces. Writing the expression representing relation between millilitres and fluid ounces

Number of milliliters = 30×64

Performing multiplication between the numbers 30 and 64

Number of milliliters = 1920

Therefore, on drinking 64 fluid ounces by Kamryn on her doctor's recommendation will drink 1920 millilitres of water everyday.

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Answer:

Answer down below!

Step-by-step explanation:

Your answer would be -3/2y + (-1/2)

If you need the steps, refer to the image below!

xw + 5w - 17 = 0 is the required equation.

Given,

Ali buys 2 comic books a week.

After 5 weeks he has 17 comic books this year.

Solution:

Let w be weeks and c be comic books.

Since Ali buys 2 comic books a week.

1w = 2c

For 5 weeks, he would have,

5w = 10c, if he bought 2books per week.

But he had 17 books,

i.e, he would have collected some books last year.

Let x be the no of unknown weeks last year.

(x + 5)w = 17c

(x+5)w-17c= 0

xw + 5w - 17 = 0 is the required equation.

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Answer:

DB is a perpendicular of AC

Answer:

u = -153

Step-by-step explanation:

u/3 = -51

multiply both sides by 3:

3(u/3) = 3(-51)

u = -153

Answer: 6

Step-by-step explanation:

-n plug -6 in so -(-6)=6

Answer:

boo ba loob

Step-by-step explanation:

sweating in saucy bbq sauce

ANSWER:

STEP-BY-STEP EXPLANATION:

The number line having -2.4 and -2.8 is attached below

Integers are arranged at equal intervals along horizontal straight lines called number lines. A number line can be used to represent every number in a series. The endpoints of this line go on forever. Some will have a defined beginning and end. We refer to these as closed number lines. Number lines may alternatively be left empty or blank. A number ladder is a vertical number line.

Given number: −12/5 and –2.8

As, we can write -12/5 in decimal form= -2.4

Now, we have to put the number on the number line

As, -2.4 lies between -2 and -3 on the left side of zero.

and, -2.4 lies between -2.5 and -3.0 on the left side of zero.

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Answer:

Explanation:

We were given the function:

We are to find the derivative of this function, we have it shown below:

Answer: 70% is percentage increase

Step-by-step explanation:

230-140/140 x 100 =90/140 x100 =0.7 x 100=70

Answer:

• Equations

• Solutions (2, 4) and (–1, 1)

Explanation

System of equations

• Linear equation

• Quadratic equation

We have to set both equations to 0 and equalize them:

• 1. Setting them to 0:

• 2. Equalizing them:

To solve the system using the General Quadratic Formula, we have to set the equation in the form ax² + bx+ c = 0:

Thus, in this case a = 1, b = -1 and c = -2. Using the formula:

Finding both solutions:

Finally, replacing these values in the linear equation to find y:

Therefore, the solutions are (2, 4) and (–1, 1).