Juan recorded the total number of free throws he attempted during practices. His results are shown in the table.
Total Number of Free
Throws Attempted (y)
Number of
Practices (x)
1
234
45
80
115
150
Juan's coach told him to attempt 10 free throws before the first practice and then 35 free throws each practice. Did Juan follow his coach's instructions?
OYes, his free throws can be represented by y 35x + 10.
OYes, his free throws can be represented by y = 45x.
No, his free throws can be represented by y = 35x.
No. his free throws can be represented by y = 45x.

The equation represents the line that has a slope of 3 and passes through the point (-4,-7) is Y = 3X - 5.

The equation of a line is a mathematical expression that describes the relationship between the x and y coordinates of any point on the line.

The slope of a line is the steepness of the line and can be calculated by finding the ratio of the change in y to the change in x for any two points on the line. In this case, the slope of the line is 3. The line also passes through the point (-4,-7), which means that we can use this point to find the equation of the line.

To find the equation of the line, we need to use the slope-intercept form, which is given by

=> Y = mX + b,

where m is the slope and b is the y-intercept. To find the y-intercept, we can use the point (-4,-7) and substitute it into the equation:

=> -7 = 3 * -4 + b.

Solving for b, we find that b = -5.

Therefore, the equation of the line is Y = 3X - 5.

So, the correct answer is b. Y = 3x + 5.

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4.571 billion years is equals to  1.4415 × 10⁷ seconds.

To calculate the number of seconds in 4.571 billion years, we first need to determine how many seconds there are in a year. There are 60 seconds in a minute, 60 minutes in an hour, 24 hours in a day, and 365 days in a year. Multiplying these together gives us 31,536,000 seconds in a year.

Next, we multiply the number of seconds in a year by the number of years in 4.571 billion years. This gives us:

31,536,000 seconds/year x 4,571,000,000 years = 1.4415 × 10¹⁷ seconds

Therefore, there are approximately  1.4415 × 10¹⁷ seconds  in 4.571 billion years.

It's worth noting that this calculation assumes a standard year of 365 days. In reality, a year is slightly longer than 365 days, and so the actual number of seconds in 4.571 billion years would be slightly higher. Nonetheless, this calculation provides a good approximation.

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Answer: 9/56

Step-by-step explanation:

44 °F was found out to be equivalent to approximately 6.67 °C using conversion formula of Fahrenheit to Celsius.

To convert a temperature from Fahrenheit to Celsius, you can use the following formula:

°C = (°F - 32) x 5/9

where °C is the temperature in Celsius, and °F is the temperature in Fahrenheit.

Using this formula, we can convert 44 °F to Celsius as follows:

°C = (44 - 32) x 5/9

= 12 x 5/9

= 6.67 °C (rounded to two decimal places)

Therefore, 44 °F is equivalent to approximately 6.67 °C.

On the Fahrenheit scale, water freezes at 32 degrees Fahrenheit (°F) and boils at 212 °F, at standard atmospheric pressure.

On the Celsius scale, the freezing point of water is defined as 0 degrees Celsius (°C), and the boiling point of water is defined as 100 °C, at standard atmospheric pressure.

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The value of x in the triangle is 10 units

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

The triangle

On the triangle, we have the following equivalent ratio

x : 15 = 4 : 6

Express as fraction

So, we have

x/15 = 4/6

This gives

x = 15 * 4/6

Evaluate

x = 10

Hence, the value of x is 10

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Step-by-step explanation:

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The speed of the river is given as follows:

4 kilometers per hour.

The lowest speed that can be assumed by the boat is given as follows:

8 - r.

In which r is the speed of the river.

The lowest velocity is of 4 kilometers per hour, hence the speed of the river is obtained as follows:

8 - r = 4

r = 8 - 4

r = 4 kilometers per hour.

Then the maximum velocity is of:

8 + 4 = 12 kilometers per hour.

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A multiple intelligences test is an assessment that identifies an individual's strengths and weaknesses across different types of intelligence, as defined by Howard Gardner's theory of multiple intelligences.

The test aims to help individuals understand their unique strengths and learning styles, and to guide educators in developing personalized teaching strategies. Multiple intelligences test is an assessment that identifies an individual's strengths and weaknesses across different types of intelligence, as defined by Howard Gardner's theory of multiple intelligences. The test is designed to go beyond traditional IQ tests, which focus on logical-mathematical and linguistic intelligence, and assess a wider range of abilities, such as musical, spatial, bodily-kinesthetic, interpersonal, and intrapersonal intelligence. The test is intended to help individuals better understand their unique strengths and learning styles, and to guide educators in developing more personalized teaching strategies that cater to a diverse range of intelligences.

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As a rule of thumb, altitude corrections of less than 100 feet should be corrected by using "less than a full bar width on the attitude indicator".

C. is the answer.

The attitude indicator (also known as an artificial horizon) is a key instrument in an aircraft that displays the aircraft's pitch and bank attitude. The instrument typically consists of a gyro that indicates the aircraft's attitude relative to the horizon.

When flying an aircraft, it's important to maintain a specific altitude, and to make adjustments as needed to stay on course. The altitude is typically measured in feet above sea level, and can be affected by a number of factors, such as temperature, pressure, and wind.

As a rule of thumb, altitude corrections of less than 100 feet can be corrected using the attitude indicator by making adjustments that are less than a full bar width on the instrument. This means that the correction is relatively small and does not require a significant adjustment of the aircraft's pitch or bank.

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The graph of a piecewise-defined function y=c is a horizontal line reaching height c from the x-axis.

A piecewise function is arithmetic that is constructed from bits of various functions across various time intervals.

To determine which of the above intervals (as well as inequalities) -

Keep in mind that the function is represented by the line y=1 and is from -∞ to 0, or the left side.

Similar to that, the function is y=-1 from 0 to ∞ (doesn't include) .

Hence, the rule provides the function:

y=1, for x≤0,

y=-1, for x>0.

Thus, the graph of a function y=c is a horizontal line reaching height c from the x-axis.

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The complete question is-

The graph of a piecewise-defined function is shown below.

Check the correct option-

On the interval (x≤0, x≤1, x<1, x<0) the function is given by the rule (x= - 1, y= - 1, y=1, x=1), and on the interval (x≥0, x>1, x≥1, x>0) the function is given by the rule (y= - 1, x= - 1, y= 1, x= 1).

The equation of the context is, 3.5x + 2y = 42 and

The y-intercept is when x = 0, indicating that no funnel cakes were purchased, and the x-intercept is when y = 0, indicating that no deep-fried Oreos were purchased.

A straight line on the coordinate plane is represented by a linear function. As an illustration, the equation y = 3x – 2 depicts a linear function because it is a straight line in the coordinate plane.

Any function whose graph is not a straight line is said to be nonlinear. Any curve other than a straight line can be a graph of it.

An example of a non-linear function is a quadratic function.

From, The given information the equation can be modeled as,

3.5x + 2y = 42.

The x-intercept is when y = 0 which states no deep fried oreos bought and the y-intercept is when x = 0, states no funnel cakes bought.

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Answer: SSS (Side- Side- Side) Congruence Postulate

Step-by-step explanation:

The point (- 1, 2) lies on the new graph.

A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.

Given that;

The graph of f(x) = |x| has been translated left 2 units and up 1 unit.

Now, The function is,

⇒ f (x) = |x|

After translated 2 unit left we get;

⇒ f (x) = |x + 2|

And, After translated 1 unit down we get;

⇒ f (x) = |x + 2| + 1

Now, We can check all the given points as;

For point (- 1, 2);

Put x = -1 , f (x) = 2;

⇒ f (x) = |x + 2| + 1

⇒ 2 = |- 1 + 2| + 1

⇒ 2 = 1 + 1

⇒ 2 = 2

Thus, The point (- 1, 2) lies on the new graph.

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Answer:

2,735 yes votes

Step-by-step explanation:

First we have too determine the ratio of yes votes to the total number of votes.

We can rationalize thus

If there are 5 yes votes and 4 no votes, the total number of votes = 5+ 4 = 9

So 5/9th of the total votes are yes votes

If the total number of votes = 4923 , number of yes votes = 5/9 x 4923

= 2,735 yes votes       ANSWER

We can check to see if our reasoning is correct:

Total number of no votes = 4923 - 2735 = 2188

Yes votes to Nay votes = 2735 : 2188

As a fraction:
2735 / 2188 = 1.25

1.25 = 1 1/4 = 5/4 which is the ratio of yes to no votes and tallies with the question data

The weight 69.9 kg is equal to approximately 154.32 pounds. This conversion was done using the formula 69.9 kg x 2.20462 lbs/kg = 154.32478 lbs.

We know that 1 kg is equivalent to 2.20462 pounds, which means that we can convert kilograms to pounds by multiplying the weight in kilograms by the conversion factor 2.20462.

So to convert 69.9 kg to pounds, we can use the following formula:

69.9 kg x 2.20462 lbs/kg = ? lbs

Multiplying 69.9 by 2.20462 gives us:

69.9 x 2.20462 = 154.32478

Therefore, 69.9 kg is equivalent to 154.32478 pounds.

Finally, we can round this result to two decimal places to get:

69.9 kg is approximately equal to 154.32 pounds.

So the final answer is that 69.9 kg is equivalent to approximately 154.32 lbs.

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If Two high schools, A and B, are each trying to raise at least $3,000 for new computers. The inequality  for each school is : x ≥ 250, x ≥ 233.33.

1. For School A, the inequality representing the number of stuffed bears they must sell to reach their goal is:

500 + 10x ≥ 3000

10x ≥ 2500

x ≥ 250

Where:

x = number of stuffed bears they must sell.

For School B, the inequality representing the number of stuffed monkeys they must sell to reach their goal is:

1250 + 7.5x ≥ 3000

7.5x ≥ 1750

x ≥ 233.33

Where:

x= number of stuffed monkeys they must sell.

2. To compare the minimum number of stuffed animals each school must sell, we round up the number of stuffed animals for School B to the nearest whole number:

x ≥ 234 for School B

Since 234 > 250, School B must sell more stuffed animals to reach their goal of $3,000.

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The quadrilateral with diagonals that are always perpendicular bisectors of each other is a square. Correct option is 1.

In a square, the diagonals bisect each other at right angles, which means they intersect at a 90-degree angle. Moreover, since a square has four congruent sides and four right angles, the diagonals are also congruent. Thus, each diagonal is a perpendicular bisector of the other diagonal, splitting it into two equal segments.

In contrast, a rectangle has diagonals that bisect each other, but they are not always perpendicular. A trapezoid has only one pair of opposite sides that are parallel, and its diagonals do not bisect each other.

A parallelogram has opposite sides that are parallel, but its diagonals do not necessarily bisect each other or intersect at a right angle.

Therefore, the correct answer is a 1 (square).

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Answer:

90, 90, 90, 90

Step-by-step explanation:

This is because a squares angles are ALWAYS 90

Answer: All 90 degrees

Step-by-step explanation:

The tangent of the smaller acute angle in a right triangle is tanФ = 5/12 taking side 5 as opposite side and 12 as adjacent side.

We know a right-angled triangle has three sides they are -: Hypotenuse,

Opposite and Adjacent or (base and perpendicular)

The Formula of tangent is opposite side/ adjacent side

Given, a right triangle with side lengths 5, 12, and 13.

We can see that largest side i.e., 13 is a hypotenuse of triangle and other two sides are base and perpendicular length.

Tangent taking side 5 as opposite side and 12 as adjacent side

tanФ = 5/12.

Tangent taking side 12 as opposite side and 5 as adjacent side

tanФ = 12/5

so, the  tangent of the smaller acute angle in a right triangle is 5/12.

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Hence, combine all the solutions we get,

[tex]x=\frac{\pi}{2} +2n\pi,x=\frac{3\pi}{2} +2\pi n ,[/tex][tex]x= sin^{-1} (\frac{1}{3} )+ 2\pi n ,x= sin^{-1 }(\frac{1}{3})+2\pi n[/tex].

Trigonometric identities are equalities which involves trigonometric functions which are true for every value of variables that occur on both sides of the identities.

Given,[tex]3\sin \left(2x\right) = 2\cos \left(x\right)[/tex]

[tex]3\sin \left(2x\right)-2\cos \left(x\right)=0[/tex]

Using trigonometric identities, [tex]sin2x= 2sinx cosx[/tex]

we get,[tex]-2\cos \left(x\right)+6\cos \left(x\right)\sin \left(x\right)=0[/tex]

Taking [tex]2cos(x)[/tex] as factor, we get,

⇒[tex]2cos(x)(3sin(x) -1)[/tex]

⇒[tex]2cos(x) = 0 , (3sin(x) -1)=0[/tex]

⇒[tex]cos (x)= 0[/tex] for x= [tex]x=\frac{\pi}{2} +2n\pi,\frac{3\pi}{2} +2\pi n[/tex] and

[tex](3sin(x) -1)=0 for x= sin^{-1} (\frac{1}{3} )+ 2\pi n , sin^{-1 }(\frac{1}{3})+2\pi n[/tex]

Hence, combine all the solutions we get,

[tex]x=\frac{\pi}{2} +2n\pi,x=\frac{3\pi}{2} +2\pi n ,[/tex][tex]x= sin^{-1} (\frac{1}{3} )+ 2\pi n ,x= sin^{-1 }(\frac{1}{3})+2\pi n[/tex].

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The number of unit cubes whose dimensions are 3/5 inch fill up the rectangular prism is (125/27)abc.

The total volume, in cubic inches, is represented in the diagram n cubic inches.

A cube is a three-dimensional object who has six faces.

Since each side of the unit cube has a length of 1 inch, the number of unit cubes that fill up the rectangular prism is equal to its volume in cubic inches. If the rectangular prism has dimensions a x b x c inches, then its volume is V = abc cubic inches.

Now, we need to find how many unit cubes whose dimensions are 3/5 inch fill up the rectangular prism. First convert the dimensions of the unit cube and the rectangular prism to a common unit, such as inches. Since 1 inch = 5/3 unit cubes, each side of the unit cube has a length (3/5) inch. Therefore, each side of the rectangular prism has dimensions (5a/3) x (5b/3) x (5c/3) unit cubes.

To find the number of unit cubes that fill up the rectangular prism, we can divide its volume (abc cubic inches) by the volume of each unit cube, which is (3/5)³ cubic inches. Thus, the number of unit cubes whose dimensions are 3/5 inch that fills up the rectangular prism is:

(abc) / [(3/5)³] = (125/27)abc

To find the total volume represented in the diagram, we need to add up the volumes of all the unit cubes shown in the diagram. Since we don't know the dimensions of the rectangular prism, we can't calculate its volume directly.

Therefore, the total volume represented in the diagram is n cubic inches.

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This is not a random sample of the restaurant's customers.

The offer of a coupon in exchange for completing a brief survey about favorite desserts may bias the sample and result in a non-random sample of the restaurant's customers.

Only those customers who were interested in the coupon may have participated in the survey, which may not be representative of the overall customer population. Additionally, those who chose to participate may have different tastes and preferences compared to those who did not participate.

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The value of x where both curve and line intersect with each others are -0.44 and 1.69

Using the linear-quadratic system, both curve and line are intersecting in 2 points where:

f(x) = g(x)

8x2 - 13x + 8 = 14 - 3x

8x2 - 10x - 6 = 0

We will use the ABC theorem, where:

x = -b ± √(b2 - 4ac)

               2a

x = - (-10) ± √((10)2 - 4(8)(-6))

                  2(8)

x = 10 ± √(100 + 192)

             16

x = 10 ± 2√73

           16

x1 = 10 - 2√73  = -0.44

           16

x2 = 10 + 2√73 = 1.69

             16

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Answer:

it is 60

Step-by-step explanation:

you add all the numbers than you round it, the number is 0 so it stays the same, hope it helps, murdle

The mean of the stem and leaf plot and the meaning of this mean is B. 3.875 feet; The value means that a typical throw of the ball results in 3.875 feet.

To find the mean, add up all the values of feet that the heavy ball was thrown in the air and then divide by the number of times the ball was thrown.

The mean is therefore :

= ( 20 + 22 + 25 + 31 + 33 + 34 + 41 + 41 + 45 + 50 + 56 + 67 ) / 12

= 465 / 12

= 38. 75 ft

This mean is the value that the typical throw of the ball results in.

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Answer: 38

Step-by-step explanation:

Subtract 1/8 from 1/2

12 - 18 is 38.

Steps for subtracting fractions

Find the least common denominator or LCM of the two denominators:

LCM of 2 and 8 is 8

Next, find the equivalent fraction of both fractional numbers with denominator 8

For the 1st fraction, since 2 × 4 = 8,

12 = 1 × 42 × 4 = 48

Likewise, for the 2nd fraction, since 8 × 1 = 8,

18 = 1 × 18 × 1 = 18

Subtract the two like fractions:

48 - 18 = 4 - 18 = 38

The required values are;

(2). x = 88°

(3). x = 5.

Angles inside a polygon are referred to as interior angles. A triangle, for instance, has three internal angles. Interior angles are sometimes defined as "angles confined in the interior area of two parallel lines when they are crossed by a transversal."

Given:

(2). The exterior angle is 52°.

So, the sum of all the interior angles in the polygon = (5 - 2)180

x + (180 - 52) + 2x + x + 2 + 90 = 560

4x + 208 = 560

4x = 352

x = 88

(3). From the diagram of the triangle,

12x - 20 = 2 (3x + 5)

12 x - 6x = 10 + 20

6x = 30

x = 5

Therefore, the values are x = 88 and x = 5.

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The slope of the line is -1/4, So correct option is B.

It is defined as the ratio of the change in the vertical coordinate (y) to the change in the horizontal coordinate (x) between any two points on the line or curve. The letter m is typically used to indicate a line's slope.

The formula for the slope of a line between two points (x1, y1) and (x2, y2) is:

m = (y2 - y1) / (x2 - x1)

The slope can be positive, negative or zero, depending on the direction of the line. A positive slope indicates that the line is moving upwards from left to right, while a negative slope indicates that the line is moving downwards from left to right. A slope of zero indicates that the line is horizontal.

The slope of a line passing through two points (x1, y1) and (x2, y2) is given by:

slope = (y2 - y1)/(x2 - x1)

Using the coordinates (-4, 2) and (4, 0), we have:

slope = (0 - 2)/(4 - (-4)) = -2/8 = -1/4

Therefore, the answer is option B, -1/4.

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The formula for converting Celsius (°C) to Fahrenheit (°F) is °F = (°C × 9/5) + 32. To convert 37 degrees Celsius to Fahrenheit, you must multiply 37 by 9/5 and then add 32.

The calculation is: 37°C × 9/5 = 66.6 and 66.6 + 32 = 98.6°FTherefore, 37 degrees Celsius is equal to 98.6 degrees Fahrenheit.The formula for converting Celsius (°C) to Fahrenheit (°F) is °F = (°C × 9/5) + 32. To convert 37 degrees Celsius to Fahrenheit, you must multiply 37 by 9/5 and then add 32. To convert Celsius to Fahrenheit, the formula is simple and easy to remember. Multiply the Celsius temperature by 9/5, then add 32. This formula is useful for many applications, such as measuring air and water temperature, cooking and baking, and more. Knowing how to convert from Celsius to Fahrenheit is important for many everyday tasks.

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Answer:

50.24

Step-by-step explanation:

c=[tex]2\pi R[/tex]=[tex]d\pi[/tex]=16*3.14=50.24