You started on a bike trip, riding at a rate of 9 miles per hour. Your friend left one hour later and rode at the rate of 12 miles per hour. How long did it take your friend to catch up with you?

The required measure of the angle Ф is given as Ф = 69.36°.

As mentioned in the question, a central angle θ of a circle with a radius of 16 inches subtends an arc of 19.36 inches.

Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.

here,
Angle = [arc/radius] 180/π
Substitute the values in the above equation,
Ф = [19.36/16]180/3.14
Ф = 69.36°

Thus, The required measure of the angle Ф is given as Ф = 69.36°.

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Answer:

If a unit fraction has a repeating decimal, its multiples will also have repeating decimals. Division by the same divisor generates the same repeating pattern. Thus, multiples cannot avoid repetition.

Explanation:

If the decimal form for a unit fraction (a fraction where the numerator is 1) is a repeating decimal, then its reciprocal (the fraction obtained by flipping the numerator and denominator) will also be a repeating decimal. This is a consequence of the way division works.

For example, if [tex]\( \frac{1}{3} \)[/tex] is a repeating decimal (0.333...), then [tex]\( \frac{3}{1} \)[/tex] (which is [tex]\( 3 \times \frac{1}{3} \)[/tex] ) will also be a repeating decimal because dividing 3 by 1 will result in the same repeating pattern.

So, no matter how you multiply a unit fraction that has a repeating decimal representation, the resulting decimal will still be repeating. Therefore, it is not possible for a multiple of that fraction to have a decimal form that is not a repeating decimal.

Answer:

B is the correct answer , B. 10,24,26

Step-by-step explanation:

Answer:

∠WXZ = 52.5

Step-by-step explanation:

Angle Bisector is the line that divides that angle into two equal parts.

Hence, Ray XZ divide the ∠WXY into two equal parts.

⇒ [tex]\angle WXZ = \frac{1}{2} \angle WXY [/tex]

∴ [tex]\angle WXZ =\frac{1}{2}\times105^{\circ}=52.5[/tex]

⇒ ∠WXZ = 52.5

An angle bisector divides an angle into two equal parts.

The measure of [tex]\angle WXZ[/tex] is [tex]52.5^o[/tex]

Given that:

[tex]XZ \to[/tex] Bisector of [tex]\angle WXY[/tex]

[tex]\angle WXY = 105^o[/tex]

This means that:

[tex]\angle WXY = 2 \times \angle WXZ[/tex]

So, we have:

[tex]105^o = 2 \times \angle WXZ[/tex]

Divide both sides by 2

[tex]52.5^o = \angle WXZ[/tex]

Rewrite as:

[tex]\angle WXZ = 52.5^o[/tex]

Hence, the measure of [tex]\angle WXZ[/tex] is [tex]52.5^o[/tex]

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After the addition of sand in the sandbox the total amount of sand in the sandbox will be equal to 21900 grams.

The four basic operations of arithmetic can be used to add, subtract, multiply, or divide two or even more quantities.

They cover topics like the study of integers and the order of operations, which are relevant to all other areas of mathematics including algebra, data processing, and geometry.

As per the given information in the question,

Total amount of sand in the sandbox = 14,500 grams

Then, James adds 7400 grams more to the sandbox.

So,

The total amount of sand in the sandbox will be,

= 14500 + 7400

= 21900 grams.

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Your questions seem incomplete, so the complete question may be:

Jim has 19,700 g of sand in his sandbox. He brings home another 6,300 g of sand from the beach to add to his sandbox.

How many kilograms of sand does Jim have in his sandbox now?

5 days x 8 hours per day  = 40 hours total

300/40 = $7.50 per hour

The hourly rate for students will be $7.5 per hour.

Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,

Summation = addition of two or more numbers or variable

For example = 2 + 8 + 9

Subtraction = Minus of any two or more numbers with each other called subtraction.

For example = 4 - 8

Division = divide any two numbers or variable called division.

For example 4/8

Multiplication = to multiply any two or more numbers or variables called multiplication.

For example 5 × 7.

Given,

Number of days working in one week = 5 days

Number of hours working in one day = 8 hour

So,

A number of hour working in one week = 5 × 8 = 40 hours.

Now

Hourly rate of pay = Earning per week/number of hours working per week

Hourly rate of pay = 300/40 = $7.5.

Hence "The hourly rate for students will be $7.5 per hour".

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The given equation is a linear equation in standard form. It can be solved for 'y' by isolating 'y' on one side. The resulting 'y' expression represents a straight line in a 2D coordinate system.

The equation 3/5 x + 1.4 y = 2/5 is a linear equation in the standard form a*x + b*y = c. In this equation, 'x' and 'y' are variables, '3/5' is the coefficient of 'x', '1.4' is the coefficient of 'y', and '2/5' is a constant.

To solve this equation, we can neatly isolate 'y' by subtracting '3/5 x' from both sides of the equation which would give us 1.4*y = -3/5*x+2/5. Then, we could further simplify by dividing both sides by '1.4', giving the equation for 'y' in terms of 'x'.

Note that this equation represents a straight line in a coordinate system. The value of 'x' and 'y' would depend on the specific problem's constraints or where this line intersects with another line in a system of linear equations.

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25*2 = 50

80-50 =30

30 /2 = 15

Answer is B

To calculate the time it takes to fill a tank using a well pump that pumps at 8.4 gallons per minute, divide the tank's volume (in gallons) by the pump's output rate (8.4 gallons per minute). For example, for a tank with a volume of 84 gallons, it would take about 10 minutes to fill.

The time it takes to fill the tank with a well pump pumping at a rate of 8.4 gallons per minute depends on the size of the tank, which wasn't specified in your question. However, to calculate this, you would use the formula: Time = Volume / Rate. If 'Volume' is the size of your tank in gallons and 'Rate' is the rate the well pump can pump water in gallons per minute (8.4 in this case), you would divide the 'Volume' by the 'Rate' to get the time it would take to fill the tank in minutes.

For example, if your tank has a volume of 84 gallons, using our formula: Time = Volume / Rate, it would translate to Time = 84 / 8.4. This gives us a duration of 10 minutes.

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40 x 5280 = 211200 feet per hour

211200 / 3600 = 58.666 = 59 feet per second

The fraction 9/4 can be written as a decimal by performing the division, resulting in 2.25. As this is already to three decimal places, the answer is 2.250.

To write the fraction 9/4 as a decimal, you simply need to perform the division operation. Dividing 9 by 4 will give you the decimal. Using a calculator or long division, the result is 2.25.

However, your question asks for the answer to be rounded to three decimal places. Since 2.25 already falls within that criteria, there's no need for further rounding. Therefore, 9/4 as a decimal, rounded to three decimal places, is 2.250.

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The equation of the circle will be x² + (y + 3)² = 4. Then the correct option is C.

A circle can be characterized by its center's location and its radius's length.

Let the center of the considered circle be at the (h,k) coordinate.

Let the radius of the circle be 'r' units.

Then, the equation of that circle would be:

(x - h)² + (y - k)² = r²

The center of the circle is at (0, -3) and the radius of the circle is 2 units. Then the equation of the circle will be

(x - 0)² + (y - (-3))² = 2²

         x² + (y + 3)² = 4

Then the correct option is C.

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Answer:

  B.  0.0000000861

Step-by-step explanation:

The exponent of -8 tells you the leading digit (8) goes in the 8th spot to the right of the decimal point. The number is ...

[tex]0.0000\,0008\,61[/tex]

Answer:

1.41421356237 making it a terminating decimal.

Step-by-step explanation:

2.82842712475

+

7.07106781187

-

8.48528137424

1.4  or 1.41

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