A cyclist rode 40 miles before having a flat tire and than walking 5 miles to a service station. The cycling rate was four times the walking rate. The time spent cycling and walking was 5 hours. Find the rate at which the cyclist was riding.

Answer: 7

Step-by-step explanation:

Since there are 42 tubes and each tray can hold 6 tubes, it will be 42/6 which is 7.

Answer:

\(\approx 91^\circ\)

Step-by-step explanation:

The given equation to represent the model for the relationship between \(x\) and \(y\).

\(y=6.88x-199\)

\(x\) represents the air temperature in degrees and

\(y\) represents the number of visitors at a pool.

Also given that number of visitors at the pool on a particular day is 426.

To find:

The expected air temperature as per the number of visitors.

Solution:

Here, we are given a linear equation to represent the relation between two variables.

Value of one variable is given and we have to find the value of other variable.

i.e. we are given that:

\(y=426\) and we have to find the value of \(x\).

Let us put the value in the equation:

\(426=6.88x-199\\\Rightarrow 6.88x = 426 + 199\\\Rightarrow x = \dfrac{625}{6.88}\\\Rightarrow \bold{x \approx 91^\circ}\)

Answer:

Step-by-step explanation:

Farmer Ed has 1,000 meters of​ fencing, and wants to enclose a rectangular plot that borders on a river. If Farmer Ed does not fence the side along the​ river, what is the largest area that can be​ enclosed?

Answer:

  5.5 cm

Step-by-step explanation:

You want the inside diameter of a conduit with an outside diameter of 6.3 cm and a wall thickness of 0.4 cm.

There is a wall at each end of the inner diameter, so it will differ from the outside diameter by twice the wall thickness:

  6.3 cm - 2×0.4 cm = 5.5 cm

The inside diameter is 5.5 cm.

Answer:

76ft^3

Step-by-step explanation:

Volume of a cube is Length x Width x Height, basically: 4 x 4 x 4 which is 64 ft^3. Add that to the small box gives you 64 + 12 or just 76 ft^3

The value of the expression \(2(cos^4 60 + sin^4 30) -(tan^2 60 + cot^2 45) + 3\times sec^2 30 is 33/4.\)

Let's simplify the expression step by step:

Recall the values of trigonometric functions for common angles:

cos(60°) = 1/2

sin(30°) = 1/2

tan(60°) = √(3)

cot(45°) = 1

sec(30°) = 2

Substitute the values into the expression:

\(2(cos^4 60 + sin^4 30) - (tan^2 60 + cot^2 45) + 3sec^2 30\)

= \(2((1/2)^4 + (1/2)^4) - (\sqrt{(3)^2 + 1^2} ) + 3(2^2)\)

= 2(1/16 + 1/16) - (3 + 1) + 3*4

= 2(1/8) - 4 + 12

= 1/4 - 4 + 12

= -15/4 + 12

= -15/4 + 48/4

= 33/4

Therefore, the value of the expression \(2(cos^4 60 + sin^4 30) -(tan^2 60 + cot^2 45) + 3\times sec^2 30 is 33/4.\)

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Answer:

Step-by-step explanation:

2,5,9,12,7,10,6,3,6

mean=(2+5+9+12+7+10+6+3+6)/9

=60/9

=6.67(approx)

Answer:

Solve all the equations.

2+n = 6

n = 4

n + 6 = 12

n = 6

4 × n = 24

n = 6

n × 3 = 2

n = 2/3

The bold equations are the answers.

Hope this helps :)

Step-by-step explanation:

Answer:

all other than the 3rd one

Step-by-step explanation:

16 quarts is equal to 4 gallons.

The correct option is C.

To convert quarts to gallons, we divide the number of quarts by 4 (since there are 4 quarts in a gallon).

Given that we have 16 quarts, we can calculate:

16 quarts / 4 quarts/gallon

= 4 gallons

Therefore, 16 quarts is equal to 4 gallons.

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The solution of the system equation is C) There is no solution

What is system equation?

  A set of one or more equations comprising numerous variables is referred to as a system of equations. The variable mappings that satisfy all of the component equations in a system of equations, or the points where the components of this system of equations intersect, are the solutions to that system. A system of equations in algebra is made up of two or more equations that are solved together. the process of eliminating, substituting, and graphing solutions to a system of equations or inequalities in two variables

Here the given equations are ,

=> y+7=3x-------> 1

=> y = 3x-7 ------> 2

and 6x-2y =12------> 3

Now put value of 2 into 3 then,

=> 6x-2(3x-7)=12

=> 6x-6x+14=12

=>14=12

The statement is false for any real number.

Therefore the correct option for the given system equation  is C) There is no solution.

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Answer:

  y = {-1/2x +7 for x < 6; 1/2x +1 for x ≥ 6}

Step-by-step explanation:

You want y = 1/2|x -6| +4 written as a piecewise function.

The absolute value function changes its definition when its argument is negative:

  y = |x|   ⇒   y = -x for x < 0, and y = x for x ≥ 0

This means our piecewise function will have one definition for (x-6) < 0 and another for (x -6) ≥ 0.

The argument is negated in this domain, so we have ...

  y = -1/2(x -6) +4

  y = -1/2x +3 +4

  y = -1/2x +7

The absolute value function is an identity function in this domain:

  y = 1/2(x -6) +4

  y = 1/2x -3 +4

  y = 1/2x +1

Combining these descriptions into one, we have ...

  \(\boxed{y=\begin{cases}-\dfrac{1}{2}x+7&\text{for }x < 6\\\\\dfrac{1}{2}x+1&\text{for }x\ge6\end{cases}}\)

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Answer:

The art teacher needs 73 containers to store all the colored pencils.  

Step-by-step explanation:

1,314 colored pencils ÷ 18 pencils per container = 73 containers total

The number of containers the art teacher need to store all the colored pencils is 73.

Given that, the art teacher buys containers to store 1,314 colored pencils.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Here, each container holds 18 pencils.

Number of containers = Total number of pencils/Number of pencils in each container

= 1314/18

= 73

Therefore, the number of containers the art teacher need to store all the colored pencils is 73.

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1.It is generally considered best practice for parents to discuss their intentions with their children and heirs to avoid confusion or misunderstandings.

2.As potential heirs, Brennan and Maureen had a responsibility to communicate with their parents about their estate planning and express any concerns or questions they had.

3.I have personally not had experience with a family member's will. However, I believe it is important to approach the topic of writing a will with sensitivity and empathy.

1. While it is understandable that Brennan and Maureen's parents may have wanted to keep their financial affairs private, their lack of communication may have caused confusion and disappointment for their children. Ideally, the parents should have discussed their estate planning with their children and explained the impact of the gifts on their final inheritance.

2. As potential heirs, Brennan and Maureen had a responsibility to communicate with their parents about their estate planning and express any concerns or questions they had. While it can be difficult to broach sensitive topics like death and inheritance, it is important for family members to have open and honest communication to prevent misunderstandings or disputes down the line.

3. It can be a difficult and emotional topic to discuss, but it is important to have open communication to ensure that everyone's wishes are respected and honored. It may be helpful to consult with a lawyer or financial advisor to ensure that the will is properly drafted and that everyone's needs are addressed.

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The area of the triangle, Rounded to the nearest hundredth, is approximately 132.02 cm².

The area of a triangle with the given measurements, we can use the formula for the area of a triangle using side lengths and an included angle. The formula is:

Area = (1/2) * a * c * sin(B)

where a and c are the side lengths, B is the included angle between those sides, and sin(B) represents the sine of angle B.

Let's calculate the area using the given measurements:

B = 103° (included angle)

a = 12 cm

c = 22 cm

First, we need to convert the angle from degrees to radians, as the sine function operates on radians. We can use the conversion: radians = degrees * (π/180).

B in radians = 103° * (π/180) ≈ 1.8 radians

Next, we can substitute the values into the formula:

Area = (1/2) * a * c * sin(B)

     = (1/2) * 12 cm * 22 cm * sin(1.8 radians)

Using a calculator, we can evaluate sin(1.8 radians) ≈ 0.9833.

Area ≈ (1/2) * 12 cm * 22 cm * 0.9833

       ≈ 132.02 cm² (rounded to the nearest hundredth)

Therefore, the area of the triangle, rounded to the nearest hundredth, is approximately 132.02 cm².

Among the given options, the closest match is:

b) 132 cm² (rounded to the nearest whole number)

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Answer:

u = 7

Step-by-step explanation:

The set of ordered pairs above: is a function.

The mapping diagram above: is a function.

y = x²: is a function.

The table above: is not a function.

In Mathematics and Geometry, a function is a mathematical equation which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair.

Based on the set of ordered pairs, mapping diagram, and the equation above, we can reasonably infer and logically deduce that it represent a function because the input values (domain, x-value, or independent values) are uniquely mapped to the output values (range, y-value or dependent values).

In this context, we can reasonably infer and logically deduce that the table does not represent a function because the input value (-1) has more than output values (2 and 4 respectively).

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Sam drove approximately 246 miles.

Let's start by subtracting the base fee from the total amount Sam paid to find the additional fee he incurred for the miles driven:

213.33 - 18.99 = 194.34

We know that the additional fee is 79 cents per mile, so we can set up an equation to find the number of miles Sam drove:

194.34 = 0.79x

where x is the number of miles driven.

To solve for x, we can divide both sides of the equation by 0.79:

x = 194.34 / 0.79 ≈ 246

Therefore, Sam drove approximately 246 miles.

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Answer:

x = 20, y = -3

Step-by-step explanation:

Set both equations equal to each other

\(\displaystyle y=\frac{3}{5}x-15\\\\y=-\frac{3}{4}x+12\\\\\\\\\frac{3}{5}x-15=-\frac{3}{4}x+12\\\\\frac{12}{20}x-15=-\frac{15}{20}x+12\\\\\frac{27}{20}x-15=12\\\\\frac{27}{20}x=27\\\\x=20\\\\y=\frac{3}{5}x-15\\\\y=\frac{3}{5}(20)-15\\\\y=\frac{60}{5}-15\\\\y=12-15\\\\y=-3\)

Answer:

3/4

Step-by-step explanation:

Answer:

Yes because 2(3) + 3 equals 9

Step-by-step explanation:

He correctly substituted x=3 into the equation and y=9. When working out both sides, he saw that both sides were equal to each other, so (3,9) is a solution!

Answer:Therefore, the equation of the line with a slope of 9/7 and containing the midpoint of the line segment with endpoints (2, -3) and (-6, 5) is:

y = (9/7)x + 25/7.

Step-by-step explanation:Step 1: Find the midpoint of the line segment.

The midpoint formula is given by:

Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)

Given the endpoints of the line segment as (2, -3) and (-6, 5), we can find the midpoint as follows:

Midpoint = ((2 + (-6)) / 2, (-3 + 5) / 2)

Midpoint = (-4 / 2, 2 / 2)

Midpoint = (-2, 1)

So, the midpoint of the line segment is (-2, 1).

Step 2: Write the equation of the line using the slope-intercept form.

The slope-intercept form of a line is given by:

y = mx + b

where m is the slope and b is the y-intercept.

Given the slope as 9/7, we have:

y = (9/7)x + b

Step 3: Substitute the coordinates of the midpoint to find the value of b.

Using the coordinates of the midpoint (-2, 1), we can substitute these values into the equation:

1 = (9/7)(-2) + b

1 = -18/7 + b

To find the value of b, we can solve this equation:

1 + 18/7 = b

25/7 = b

Step 4: Write the final equation of the line.

Using the value of b, the equation becomes:

y = (9/7)x + 25/7

Answer:

Domain: 0,1,2

The relation is a Function.

Step-by-step explanation:

hope this helps

A relation may or  may not be a function.

The relation is given as:

\(\mathbf{(x,y) = \{(0,0),(1,1),(2,0)\}}\)

List out the x-values

\(\mathbf{x = \{0,1,2\}}\)

The above set means that the x-values starts from 0 and ends at 2.

Hence, the domain is: [0,2]

For a relation to be a function, all y-values of the relation must point to different x-values.

So, we can say that, the given relation is a function, because all y-values have unique x values

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The function is:

C(n) = 59 + 13n

where n is the number of people, and C(n) is the cost of a class party.

To determine the value of C(n) where n = 44, just replace this value of n into the previous formula, and simplify the expression, just as folow:

C(44) = 59 + 13(44)

C(44) = 59 + 572

C(44) = 631

Hence, the cost for 44 people is 631 dollars.

The 9/32 of whole pizza Troy had for breakfast. The whole bag of coffee weighs 10/7 pounds

A fraction is defined as a part of a whole quantity.

1. Leftover pizza = 3/8

Pizza used as breakfast = 3/4 of left-over pizza

= 3/4 of 3/8

The of is calculated by the use of multiplication

The fractions are multiplied as follows:

Pizza used as breakfast = 3/4 * 3/8

= 3 * 3 / 4 * 8

= 9/32

2. 3/5 of bag of coffee weighs = 6/7 pounds

1 bag of coffee weighs = 6/7 ÷ 3/5

The fractions are divided as follows:

Thus, = 6/7 * 5/3

= 6 * 5 / 7 * 3

= 30/21

= 10/7 pounds

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Answer: x = -3/2 , x = -1 1/2 , x = -1.5

Step-by-step explanation:

6/-4.5 = 8/4x

first determine the defined range --> x ≠ 0

cancel out the common factor 4 --> 6/-4.5 = 2/x

the convert the decimal into a fraction --> 6/-9/2 = 2/x

now use -a/b = a/-b = -a/b to rewrite the fraction --> 6/-9/2 = 2/x

then simplify the complex fraction --> -4/3 = 2/x

simplify the equation using cross-multiplication --> -4x=6

divide both side of the equation by -4 --> x = -3/2 , x ≠ 0

lastly, check if the solution is in the defined range --> x = -3/2

solution : x = -3/2

Alternative form: x = -1 1/2 , x = -1.5 (simplified)