There are 162 people waiting in line to ride a roller coaster when the line closes for the day. Each roller coaster car holds 12 people. After loading c cars on the roller coaster, there are 6 people still in line. Write an equation to represent the number of cars, c, that have been loaded on the roller coaster. Solve the equation to find the number of cars on the roller coaster

Answer:

To find an equivalent expression for the area of the cement walkway, we can first distribute the 32 on the right side of the equation to get 32(5x-1 + 8) = 32(5x-1) + 32(8). Then, we can subtract the area of the courtyard, 24(5x-1), from this expression to get 32(5x-1) + 32(8) - 24(5x-1) = 8(5x-1) + 32(8). This is an equivalent expression that represents the area of the cement walkway in square yards.

the beam is constructed from two boards fastened together at the top and bottom with three rows of nails spaced every 4 in is[tex]487.5lb .[/tex]

Calculate the moment of inertia by using following expression,

\begin{aligned}

[tex]I & =\frac{1}{12} b d^3 \\& =\frac{1}{12} \times 6 \times(4)^3 \\& =32 \mathrm{in}^4\end{aligned}\\[/tex]

The centroid at center is,

[tex]\begin{aligned}Q & =\bar{y}_1 A \\& =1 \times 6 \times 2 \\& =12 \mathrm{in}^3\end{aligned}$$[/tex][tex]\begin{aligned}q & =\frac{V Q}{I} \\& =\frac{650 \times 12}{32} \\& =243.75 \mathrm{lb} / \mathrm{in}\end{aligned}$$[/tex]

The shear flow is,

[tex]\begin{aligned}q & =\frac{V Q}{I} \\& =\frac{650 \times 12}{32} \\& =243.75 \mathrm{lb} / \mathrm{in}\end{aligned}[/tex]

Since, there is 3 rows of nails so the shear force resisted by each nail is,

[tex]\begin{aligned}\tau & =\frac{1}{3} q s \\& =\frac{1}{3} \times 243.75 \times 6 \\& =487.5 \mathrm{lb}\end{aligned}$$[/tex]

Therefore, the shear force resisted by each nail is 487.5

[tex]487.5lb .[/tex]

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The volume of the cuboid is 64288 ft³

Volume of cuboid is the total space occupied by the cuboid in a three-dimensional space. A cuboid is a three-dimensional structure having six rectangular faces. These six faces of the cuboid exist as a pair of three parallel faces. Therefore, the volume is a measure based on the dimensions of these faces, i.e. length, width and height.

The formula of volume of a cuboid is given by

V = L * W * H

Substituting the values into the formula;

v = 41 * 32 * 49

v = 64288 ft³

The volume is 64288 ft³

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The option that indicates the correct volume of the rectangular prism in the photo that has the dimensions of length, 41 feet, width, 32 feet, and height, 49 feet is option a.

a. 64,288 ft³

A rectangular prism is a solid that has six rectangular faces, and twelve edges, in which each face has a parallel and congruent face on the opposite side of the prism, that has eight corners.

The dimensions of the rectangular prism in the question are;

Length of the rectangular prism = 41 feet

Width of the rectangular prism box = 32 feet

Height of the prism = 49 feet

The volume, V, of the rectangular prism is the product of the width, the length and the height as follows;

Volume of a rectangular prism, V = Width × Length × Height

The volume of the rectangular prism in the question is therefore;

V = 32 feet × 41 feet × 49 feet = 64,288 feet³

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Answer:

y = 8x

Step-by-step explanation:

The amount of sugar in grams is 8 times the number of portions.

For example, 1 portion has 8 grams of sugar.

Two portions have 16 grams of sugar.

If you let y = number of grams of sugar and x = number of portions, then

y = 8x

The income tax can be paid by the teacher =$ 9212.

An income tax is a sort of tax that is levied on the earned and unearned income of an individual or corporation.

For instance, the United States levies a federal income tax on its residents, regardless of where they reside—in the country or overseas. The majority of the money the US government receives comes from this income tax.

Here we have

The annual salary of a teacher is $ 65,800

The rate of income tax = 14%

The income tax can be paid = 14% of 65800  

=> [tex]\frac{14}{100} \times 65800[/tex]

= [tex]14 \times 658[/tex]

= 9212

Therefore,

The income tax can be paid by the teacher =$ 9212  

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Correct formatting for a nested function is

=IF(AND(B2>3000,02>2000),"Bonus","No Bonus")

A nested If statement is used when 1 or more conditions are to be tested. The result of the nested function depends based on the true value of the function.

i.e. If the nested statement is true, certain operations are to be done otherwise, do something else. In other words, the IF function allows you to make a logical comparison between a value and what you expect by testing for a condition and returning a result if True or False.

The syntax of a nested function goes thus

IF( condition1, value_if_true1, IF( condition2, value_if_true2, value_if_false2 ))

This would be equivalent to the following in Excel

= IF(condition1,"value_if_true",value_if_false)

Base on the above explanation, only option B is right.\

And what it does is that

it checks if cell B2 is greater than 3000 AND cell 02 is greater than 2000.

If both statement are true, "Bonus" will be the output result

If one ore both statement are false, "No Bonus" will be the output result

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Answer: B

Step-by-step explanation:

i just did it

Answer:

The observation in the upper right corner of the plot is influential for the least-squares regression line.

Step-by-step explanation:

Answer:

B. 80 degree

Step-by-step explanation:

These angles are same-side interior angles. Which means both angles have to add up to 180 degrees. One angle is 100 degrees; the other must be 80 degrees!

Answer:

op

Step-by-step explanation:

In order to plot the region enclosed by the given graphs we have to find the intersection points of all the 3 graphs taking 2 at a time

so finding intersection point of the y=4/x and y=16x

4/x=16x

=>  = 1/4

=> x = 1/2 as x>0

and y=16x

=> y =8

now finding intersection point of y=4/x and y=1/16x

=> 4/x =x/16

=>  = 64

=> x = 8 as x>0

and y= 4/x

=> y=1/2

now finding intersection point of y=16x and y=1/16x

the intersection point of both line is x=0

so y=16x

=> y=0

so we will get the intersection point of all the lines now after plotting all the points below we will get the graph as attached below.

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Answer:

£2.94

Step-by-step explanation:

1500g = 750g x 2 = 2 boxes

£1.96 = price for 1 box

÷ by 2 = 98p

add that to £1.96 = £2.94

The true statement is (d) the angle measures of trapezoid PQRS are equal to the corresponding angle measures of trapezoid KLMN

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

Trapezoid PQRS

The transformation is given as

As  a general rule of transformation, reflection and rotation are rigid transformations and they do not change the size and angles in a shape

This means that we get a congruent figure to that figure after the transformations

Thus, when PQRS is reflected and rotated 90° about the origin to form trapezoid KLMN, the trapezoid KLMN is congruent to trapezoid PQRS.

⇒  By the definition of congruence,

The corresponding sides and angle of trapezoid KLMN are congruent to that of trapezoid PQRS.

⇒ ∠P ≅ ∠K, ∠Q ≅ ∠L, ∠R ≅ ∠M and  ∠S ≅ ∠N

⇒ Option D) is correct.

Note:  KMLN is a trapezoid ⇒ Sum of the angle measures of trapezoid P'Q'R'S' is also 180°

Option A) is incorrect.

Since, trapezoid KMLN is congruent to trapezoid PQRS.

⇒ Option B) is incorrect.

We know that if two shapes are congruent then their area must be equal.

⇒ Area of trapezoid KMLN = Area of trapezoid PQRS

Thus, Option C) is incorrect.

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Complete question

Trapezoid PQRS is shown on the coordinate plane. If trapezoid PQRS is reflected across the y-axis and rotated 90° clockwise about the origin to form trapezoid KLMN, which must

A) The sum of the angle measures of trapezoid PQRS is 180° less than the sum of the angle measures of trapezoid KLMN.

B) Trapezoid PQRS is not congruent to trapezoid KLMN

C) The area of trapezoid PQRS is less than the area of trapezoid KLMN

D) The angle measures of trapezoid PQRS are equal to the corresponding angle measures of trapezoid KLMN

The correct expression that has a product greater than 4 is one hundred and one hundredths times four.

There are four expressions given as

(a) four hundredths of a percent

= 4 × 99/100

= 4 × 0.99

= 3.96

(b) four times the eighth

= 4 × 8/8

= 4 × 1

= 4

(c) four times three-fourths

= 3/4 × 4

= 3

(d) one hundred and one hundredths multiplied by four

= 1.01 × 4

= 4.04

As a result, the expression with a product greater than four is one hundred and one hundredths times four.

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[tex]-\cfrac{5}{7}(-42k-56)\implies -\cfrac{5}{7}(-42k)\left[ -\cfrac{5}{7}(-56) \right]\implies +\cfrac{5}{7}(42k)+\left[ \cfrac{5}{7}(56) \right] \\\\\\ \cfrac{5(42k)}{7}+ \cfrac{5(56)}{7}\implies 5\cdot \cfrac{42}{7}k + 5\cdot\cfrac{56}{7}\implies 5\cdot 6k+5\cdot 8\implies {\Large \begin{array}{llll} 30k+40 \end{array}}[/tex]

Option 2 is correct that is 1.79

When presented in ascending order, the value that 75% of data points fall within is known as the higher quartile, or third quartile (Q3).

The quartiles formula is as follows:

Upper Quartile (Q3) = 3/4(N+1)

Lower Quartile (Q1) = (N+1) * 1/3

Middle Quartile (Q2) = (N+1) * 2/3

Interquartile Range = Q3 -Q1,

1.74, 0.24, 1.56, 2.79, 0.89, 1.16, 0.20, and 1.84 are available.

Sort the data as follows: 0.20, 0.24, 0.89, 1.16, 1.56, 1.74, 1.84, 2.79 in ascending order of magnitude.

The data set has 8 values.

hence, n = 8; third quartile: 3/4 (n+1)th term

Q3 =3/4 of a term (9) term

Q3 =27/4 th term

Q3 = 1.74 + 1.84 / 2 (average of the sixth and seventh terms)

equals 1.76

Thus Q3 is 1.76 that is option 2

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The equation of the perpendicular line is y = (7/3)x - 2/3. And the slope of the line is 7/3.

Let the equation of the line be ax + by + c = 0. Then the equation of the perpendicular line that is perpendicular to the line ax + by + c = 0 is given as bx - ay + d = 0. If the slope of the line is m, then the slope of the perpendicular line will be negative 1/m.

The equation of the line is given below.

y = -(3/7)x + 4

The equation of the line that is perpendicular to y = -(3/7)x + 4 will be given as,

y = (7/3)x + d

The equation passes through (2, 4) will be given as,

4 = (7/3) × 2 + d

c = - 2/3

Then the equation of the perpendicular line is given as,

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

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The general form of an equation having vertex and point is y=a(x-h)²k. Then, the general form equation with the vertex of (-4,1) and point (-3,3) is y=3x²+24x+48.

The vertex form is an alternative way to state a parabola's equation. The equation y=a(x-h)²k is the formula for this, where k denotes the vertical translation, h is the horizontal translation, and a is a vertical stretch factor.

Here, given the vertex (h,k) is (-4,1) and the point (x,y) is (-3,3)

Start by substituting the values of h and k in the vertex equation, we get,

y=a(x+4)²(1)

Given that the point where the vertex meets is (-3,3). If we substitute this point into the equation above, we obtain,

3=a(-3+4)

a=3

To obtain the general form, now substitute the values of a and (h,k) in the vertex equation. We get,

y=3(x+4)²

y=3(x²+8x+16)

y=3x²+24x+48

Therefore, the required answer is y=3x²+24x+48.

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The percentage of the guests at this hotel who called for room service yesterday is 40%

When provided,

170 visitors in total requested room service.

The total number of visitors who did not request room service was 255.

We can now determine the overall number of guests.

Total guests equal (total guests who requested room services) plus (total number of guests who did not call for room services)

so,

there are overall guests of

=170+255

=425

We can now find the percentage

the proportion of visitors to this hotel who requested room service yesterday is

170/425 *100%

=40

The percentage of the customers at this hotel who called for room service yesterday is 40%.

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in exponential smoothing, if you would like to see the overall long-term tendency of the series, set a small weight, close to 0 is True statement.

In exponential smoothing, a weight is assigned to each data point in the series.

If a small weight is assigned, close to 0, it means that the more recent data points will have a lesser influence on the overall result.

This will therefore show the overall long-term tendency of the series.

in exponential smoothing, if you would like to see the overall long-term tendency of the series, set a small weight, close to 0 is True statement.

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Confounding variables is the term used to describe these additional factors that might have an effect on the stress levels of tea drinkers.

Confounding variables are those that have an effect on other factors in such a way that misleading or distorted relationships between two variables result. They misinterpret the "real" relationship between two variables. Confounding variable illustration You track sunburns and ice cream consumption. You discover that eating more ice cream increases your chances of becoming sunburned. To establish if a particular risk factor produced confounding, compare the estimated measure of association before and after controlling for confounding. To put it another way, compute the measure of association before and after correcting for a potential confounding factor.

Here,

Confounding variables are the terms used to explain these other elements that may have an influence on tea users' stress levels.

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An equation for the line parallel to the given line that contains C(2,4) is y = (3/4)x + (1/2).

We may use the slope-intercept version of the expression of a line, which is provided by "y = mx + b," where m seems to be the slope of the line & b is the y-intercept, to express the linear function that is perpendicular to a given line as well as contains a particular point.

We may easily utilize the same value of m again for the equation of a parallel line if the slope-intercept form of a line's equation is provided. For instance, if the provided line's equation is "y = 2x + 1," a parallel line's equation would be "y = 2x + c," where c is a constant.

By restructuring the equation in slope-intercept form if the equation of a line is provided in another form, such as "ax + by + c = 0," it is possible to determine the slope of the line. If the expression of the single sequence is "3x - 4y + 5 = 0," for instance, we may rewrite it in slope-intercept form by focusing just on y on one side of the equation:

3x - 4y + 5 = 0

-4y = -3x - 5

y = (3/4)x + (5/4)

The slope of the line is 3/4.

4 = (3/4)(2) + b

4 = (3/2) + b

b = 4 - (3/2)

b = (4 - 3/2)

b = (4 - 3)/2

b = (1/2)

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Answer:

750 ft

Step-by-step explanation:

the 2 situations are similar ( both right triangles ) with corresponding sides being in proportion.

let h be the height of the cell phone tower

We require the dimensions to be the same, using the conversion

1 foot = 12 inches , then

10 ft = 10 × 12 = 120 in

125 ft = 125 × 12 = 1500 in

then we obtain

[tex]\frac{h}{1500}[/tex] = [tex]\frac{120}{20}[/tex] =  6 ( multiply both sides by 1500 to clear the fraction )

h = 1500 × 6 = 9000 in ( divide by 12 to convert to ft )

h = 9000 in ÷ 12 = 750 ft

that is the cell phone tower is 750 ft tall.

The time that has elapsed since Gerardo started walking away from car will be equal to 5 seconds.

We solve this problem by converting it into a linear equation that has three variables in it. Since we have distance, time and speed the three variables will be d, t and s respectively. The expression which shows the distance of Gerardo will be expressed as

d = (s×t) + 9; we have the constant as 9 because Gerardo was 9 feet away from his car.

Now, we have the distance as d = 24 feet and the speed is constant that is equal to 3 feet per second and we need time which will be

24 = (3×t) + 9

15 = 3×t

=> t = 15/3

=> t = 5 seconds

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By using the property of triangle, it can be calculated that-

A triangle is possible for case b) and c)

What is a triangle?

A triangle is a three sided two dimensional figure. A triangle has three sides and three interior angles.

We know that sum of two sides of a triangle is always greater than the third side

For a)

CA + BC = 3 + 1 = 4 which is not greater than AB = 4

A triangle is not possible in this case

For b)

CA + BC = 10 + 8 = 18 > AB = 8 cm

AB + AC = 8 + 10 = 18 > BC = 8cm

AB + BC = 8 + 8 = 16 > AC = 10 cm

A triangle is possible in this case

For b)

CA + BC = 8 + 10 = 18 > AB = 7 cm

AB + AC = 7 + 8 = 15 > BC = 10cm

AB + BC = 7 + 10 = 17 > AC = 8 cm

A triangle is possible in this case

So a triangle is possible for case b) and c)

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The median score for the whole semester is 85. Thus, option a is correct.

It is given to us that -

The grades on first 7 tests of a statistics student are -

76, 80, 91, 94, 78, 85. 90

We have to find out the median score for the whole semester.

To find out the median, we have to first arrange the grades in ascending order from lowest to highest. Thus, arranging them in ascending order, we have -

76, 78, 80, 85, 90, 91, 94

Now, from this arrangement from lowest to highest, the median can be found out as the middle number in the given order which is equal to 85.

Therefore, the median score for the whole semester is 85. Thus, option a is correct.

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The probability P(A and B) has a value of (d) 0.2

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

These mean that

P(A) = 0.4

P(B) = 0.5

From the question, we have

The events are independent events

This means that

P(A and B) = P(A) * P(B)

So, we have

P(A and B) = 0.4 * 0.5

Evaluate

P(A and B) = 0.2

Hence, value is 0.2

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The slower pipe if working alone can fill the tank in 10.5 hours.

A cuboid is a three-dimensional solid that has 6 faces (rectangular), 8 vertices, and 12 edges. A cuboid has three dimensions such as length, width, and height. A perfect cuboid is said to be a cuboid that has integer edges and the formula for its volume is: V = length ×breadth× width

Given here dimensions of the swimming pool as 30 feet long, 14 feet wide, and an average depth of 8 feet, therefore the volume of the swimming pool V = 30×14×8

  = 3360 feet³

Again the two pipes working together can fill the pool in 3.5 hours and let their speeds 2x and x then, their relative speed = 3x

thus we have 3.5 = 3360/3x

                  ⇒   x  = 320 feet³/hr

Therefore the individual speeds are equal to 320 feet³/hr and 640 feet³/hr

Accordingly, the time taken by the slower pipe to fill the entire tank alone is = 3360/320

             = 10.5 hours

Hence, the time taken by the slower pipe is 10.5 hours

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Answer:

Step-by-step explanation:

so

180 = 2a + 62 + 54 - a + 5a - 20

180 = 6a + 96

180 - 96 = 6a

84 = 6a

a = 14

2a + 62 =

2 * 14 + 62 =

28 + 62 =

90°

54 - a =

54 - 14 =

5a - 20 =

5 * 14 - 20 =

70 - 20 =

60°

The linear inequality y > 3/4x - 2 is true about the graph passes through the x - axis at 2.67, the graph passes through the y - axis at -2  and the graph has a straight broken line to denote the ">" inequality sign.

Linear inequalities are inequalities that involve at least one linear algebraic expression, that is, a polynomial of degree 1 is compared with another algebraic expression of degree less than or equal to 1. To represent various kinds of linear inequalities.

In the given, we can represent this on a graph.

The graph of y > 3/4x - 2 shows these properties

The graph passes through the x - axis at 2.67 and the y - axis at -2

The graph has a straight broken line shows the ">" inequality sign.

The correct option is A.

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Complete Question:

Which of the statement are true about the linear inequality y > 3/4x - 2

I. The graph has a broken line

II. The graph has an unbroken line

III. The graph passes through y - axis at -2

IV. The graph passes through the x - axis at 2.67