To support a shelf, the diameter of a bolt can measure anywhere from 0.2 cm less than 1.5 cm to 0.2 cm greater than 1.5 cm. Which graph represents the possible measures of the diameter of the bolt?

scientific notation is the standard form of writing numbers in a particular format

scientific notation is writing a number between 0 and 10 times a power of 10

the number to be written is 427 000

so we need to get the decimal point after the first digit from the right

decimal point should come to the right of digit 4

for the decimal to come next to 4 it has to move 5 places to the left. Then its 4.27 multiplied by 10⁵

scientific notation is - 4.27 x 10⁵

Based on the information given 427 thousand as scientific notation is:4.27 x 10⁵.

Scientific notation is the way of writing or expressing number in simplest form.

4.27 x 10⁵=4.27×10×10×10×10×10

4.27 x 10⁵=427,000

Scientific expression=4.27 x 10⁵

Inconclusion  427 thousand as scientific notation is:4.27 x 10⁵.

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Final answer:

The y-intercept is the value of y when x is zero, represented by the constant b in the linear equation y = mx + b. In the example y = 55x + 75, the y-intercept is 75, indicating where the line intersects the y-axis and signaling the initial value of y before any changes in x.

Explanation:

An example of a y-intercept can be found in the linear equation y = mx + b, where b represents the y-intercept. This value is where the line crosses the y-axis on a graph. If we consider the equation y = 55x + 75, for instance, the y-intercept is 75. This means that when x (the independent variable) is zero, the y value, possibly indicating the starting point of a scenario such as labor charges before work begins, is 75.

A real-world example can be seen in a car repair scenario where the total labor charges (y) depend on the number of hours worked (x). Given the equation y = 55x + 75, when no hours are worked (x=0), the total charges start at $75, which is the y-intercept. The slope of the line is 55, indicating that for each additional hour worked, the labor charges increase by $55.

The two numbers that have a difference of 2 and a rounded difference of 100 are: 149 and 151.

When rounded to the nearest hundred, 149 rounds down to 100, and 151 rounds up to 200.

The difference between 100 and 200 is 100, which is the rounded difference between the two numbers.

149 and 151:

Difference: 151 - 149 = 2

Rounded difference: 100 - 0 = 100 (151 rounds to 100 and 149 rounds to 0)

Therefore, the two numbers that have a difference of 2 and a rounded difference of 100 are 149 and 151.

Complete question:

The difference between two numbers is 2. When each number is rounded to the nearest hundred, the difference between them is 100.

Write what the two numbers could be. (1 Point)

197 and 195

125 and 123

149 and 151

97 and 98

By dividing the total change in speed (30 miles per hour) by the total time span (10 seconds), it can be determined that Mr. Diaz decreased his car's speed by an average of 3 miles per hour each second.

In this problem, Mr. Diaz decreased his car's speed by 30 miles per hour over a span of 10 seconds. To find the average change in speed each second, we divide the total change in speed by the total time period.

So, we can calculate the average change as follows:

30 miles per hour ÷ 10 seconds = 3 miles per hour per second

Therefore, the average change in Mr. Diaz's car speed each second is 3 miles per hour.

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The expression "0.09x" represents the amount of tax that is paid on the bicycle.

Expressions are mathematical statements with a minimum of two terms containing variables or numbers.

Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.

We have been given that the expression 0.09x + (x - 30) models the final price of a bicycle with an instant rebate in a state that charges a sales tax.

⇒ 0.09x + (x - 30)

Here the tax is on the original price.

Here the tax paid on the bicycle is denoted by the term "0.09x".

Thus, the expression "0.09x" represents the amount of tax that is paid on the bicycle.

Learn more about the expression here:

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Answer:

|−70 − 13| = |−83| = −83 units

Step-by-step explanation:

The following correctly uses absolute value to show the distance.

I took the test too

Answer:

She scored 25 points in the second game more than in the first one.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Penelope has a birdhouse that is 4.9 feet above the roof of her garage.

She has a second birdhouse that is 5.36 feet below the roof of her garage.

The distance of first birdhouse from the roof = 4.9 feet

The distance of the second birdhouse from the roof = 5.36 feet

The distance between the birdhouses = 4.9 + 5.36

                                                                = 10.26 feet

Total distance between the birdhouses are 10.26 feet.

Answer:

1) Twenty-one halves of one-thirds are in seven halves.

2) Fourteen-thirds of three-fourths are in five halves.

Step-by-step explanation:

1) To find : How many one-thirds are in seven halves?

Solution :

Let the required number be 'x',

According to question,

[tex]\frac{1}{3}\times x=\frac{7}{2}[/tex]

Solving the equation,

[tex]x=\frac{7\times 3}{2}[/tex]

[tex]x=\frac{21}{2}[/tex]

Therefore, Twenty-one halves of one-thirds are in seven halves.

2) To find : How many three-fourths are in five halves?

Solution :

Let the required number be 'x',

According to question,

[tex]\frac{3}{4}\times x=\frac{5}{2}[/tex]

Solving the equation,

[tex]x=\frac{7\times 4}{2\times 3}[/tex]

[tex]x=\frac{14}{3}[/tex]

Therefore, Fourteen-thirds of three-fourths are in five halves.

Final Answers:

m∠ZOY = 60°

m∠ZOW = 180°

m∠VOW = 60°

m∠SOU = 190°

m∠TOU = 95°

m∠ZOT = 85°

Here's a step-by-step solution with the final answers:

1. Identify the given angles:

m∠UOV = 35°

m∠YOW = 120°

OT bisects ∠SOU

2. Find m∠VOW:

∠VOW and ∠YOW are supplementary angles because they form a straight line.

m∠VOW = 180° - m∠YOW = 180° - 120° = 60°

3. Find m∠ZOY:

∠ZOY and ∠VOW are vertical angles, so they are congruent.

m∠ZOY = m∠VOW = 60°

4. Find m∠ZOW:

∠ZOW and ∠YOW are adjacent angles that share a common side (OW).

m∠ZOW = m∠ZOY + m∠YOW = 60° + 120° = 180°

5. Find m∠SOU:

Since OT bisects ∠SOU, m∠TOU = 1/2 * m∠SOU.

We'll find m∠TOU later, so keep this relation in mind.

6. Find m∠TOU:

∠TOU and ∠UOV are adjacent angles that share a common side (OU).

m∠TOU = m∠VOW + m∠UOV = 60° + 35° = 95°

7. Find m∠SOU (using the relation from step 5):

m∠SOU = 2 * m∠TOU = 2 * 95° = 190°

8. Find m∠ZOT:

∠ZOT and ∠TOU are supplementary angles because they form a straight line.

m∠ZOT = 180° - m∠TOU = 180° - 95° = 85°

Final Answers:

m∠ZOY = 60°

m∠ZOW = 180°

m∠VOW = 60°

m∠SOU = 190°

m∠TOU = 95°

m∠ZOT = 85°


The probable question is in the image attached.

Answer:

7:8 (if it's in it's simplest form.) if not, then it's 80:70 :)

Step-by-step explanation:

Option: b is the correct answer.

                   b)    7.8 miles.

Let us suppose that the city center is located at C(0,0) on the coordinate grid.

Now, The mall is 2 miles east and 2 miles north of the city's center.

This means that the coordinate of  the mall is located at M(2,2)

and Truth Park is 3 miles west and 4 miles south of the city's center.

This means that the coordinate of the Truth park is located at P(-3,-4)

Hence, the distance between the mall and Truth park is equal to the sum of the distance between the Center city and mall and center city and Truth park.

i.e.   PM=CM+PC

From the figure we may observe that:

 [tex]CM=\sqrt{(2-0)^2+(2-0)^2}\\\\CM=\sqrt{4+4}\\\\CM=\sqrt{8}=2\sqrt{2}[/tex]

Hence, [tex]CM=2.828\ miles[/tex]

Similarly,

[tex]PC=\sqrt{(0-(-3))^2+(0-(-4))^2}\\\\\\PC=\sqrt{3^2+4^2}\\\\\\PC=\sqrt{9+16}\\\\\\PC=\sqrt{25}\\\\\\PC=5\ miles[/tex]

Hence, PM=2.828+5=7.828 miles

       The distance between mall and Truth park to the nearest tenth is:

                          7.8 miles

Step-by-step explanation:    

Apply Exponent Rule

[tex]a^{-b}=\frac{1}{a^b}[/tex]

[tex]=\frac{1}{8^{\frac{5}{8^{-3}}}}[/tex]

Simplify

[tex]=\frac{1}{8^{8^3\cdot \:5}}[/tex]

[tex]=\frac{1}{8^{2560}}[/tex]

Explanation in words (Short Form)

- The first step to simplify this equation (8^-5 / 8^-3) is to first apply the exponent rule then solve this equation as shown above and in the picture. Regarding back to the equation, we will then simplify it and the answer will result as 0. Without simplify the answer is as [tex]=\frac{1}{8^{2560}}[/tex].

Answer: 0: Simplified form

Answer:  

[tex]=\frac{1}{8^{2560}}[/tex]

OR

= 0

Hope this helps.