7x – 2y = 8Which equation is equivalent to it?

The volume of the cone is 13 cm³. option D

To determine the volume of the cone, we have that;

The formula for calculating the volume of a cone is expressed as;

Volume = (1/3)πr ²√(L ² - r ²).

Such that;

Substitute the values, we have;

Volume = 1/3 × 3.14 ² × √(25 - 9)

Find the squares, we get;

Volume, V = 1/3 × 9. 86 × √16

Find the square root

Volume, V = 1/3 × 9.86 × 4

Volume, V = 13 cm³

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Answer:

3x minus negative 3

Step-by-step explanation:

If you multiply 3x-4 and 3x- -3 then you would get 9x - 12.

A.

1. Mode: No mode. Median: 24. Mean: 30.875. Range: 50.

2. Mode: No mode. Median: 33.5. Mean: 43.9. Range: 85.

3. Mode: No mode. Median: 46. Mean: 43.571. Range: 61.

4. Mode: No mode. Median: 17. Mean: 18. Range: 28.

5. Mode: No mode. Median: 10.5. Mean: 13.5. Range: 27.

6. Mode: 15. Median: 22.5. Mean: 25.857. Range: 31.

B.

7. Mode: 4.3. Median: 4.2. Range: 2.1.

8. Mode: 18.6. Median: 18.6. Range: 0.8.

C.

9. Mode: No mode. Median: 4/9.

10. Mode: No mode. Median: 5/24.

Answer:

84 + 84(0.22)

Step-by-step explanation:

In order to find the amount of the tip you need to do 84x0.22 then you add that on to the original price

Answer:

-18/3x - 9

Step-by-step explanation:

-9(2/3x + 1)

Expand.

-18/3x + -9

Answer:

it depends

Step-by-step explanation:

If 17 is the hypotenuse

\(c=17\\\\b=12\\\\a=?\\\\c^{2} =a^2+b^2\\\\17^2=a^2+12^2\\\\17^2-12^2=a^2\\\\(17-12)(17+12)=a^2\\\\5(27)=a^2\\\\a=\sqrt{9*3*5} \\\\a=3\sqrt{15} \\\\a=11.6\)

if you are looking for the hypotenuse

\(a=17\\\\b=12\\\\c=?\\\\a^2+b^2=c^2\\\\17^2+12^2=c^2\\\\289+144=c^2\\\\433=c^2\\\\c=\sqrt{433} \\\\c=20.8\)

The percentage of people over speeding on this road on purpose is 9%

Percent of people speeding on this road noticed the sign = Percentage of people who notice the speed limit at the beginning of the road - Percentage of people who notice the sign and follow the speed limit

= 84% - 75%

= 9%

In conclusion, the percentage of people who intentionally speed on purpose is 9%

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Answer:

Using the formula provided, we need to calculate the following values:

- The sum of (f * x) for each interval

- The sum of (f * x^2) for each interval

- The total number of sample values (n)

Using the table provided, we can fill in the following values:

(the photo)

To calculate the standard deviation using the formula provided, we need to substitute the values into the formula:

s = sqrt((n∑(fx^2)-(∑(fx))^2)/(n(n-1)))

Plugging in the values we calculated, we get:

s = sqrt((91278136.5-(7140.5)^2)/(91(91-1)))

s = sqrt(232378.83)

s ≈ 482.1

Rounding to one decimal place, we get s ≈ 482.1

Comparing this to the given standard deviation of the original list of data values (9.0), we can see that there is a significant difference. This is likely due to the fact that the frequency distribution table only provides grouped data, while the original list of data values would provide a more precise and detailed representation of the data.

The standard deviation of the sample data from the frequency distribution table, is  85.63.

Using the given intervals, the class midpoints are:

30-39, x = (30 + 39) / 2 = 34.5

40-49,  x = (40 + 49) / 2 = 44.5

50-59,  x = (50 + 59) / 2 = 54.5

60-69,  x = (60 + 69) / 2 = 64.5

70-79, x = (70 + 79) / 2 = 74.5

80-89, x = (80 + 89) / 2 = 84.5

∑ f.x² = (5 × (34.5²)) + (20 × (44.5²)) + (36 × (54.5²)) + (16 × (64.5²)) + (10 × (74.5²)) + (4 × (84.5²))

= 922,926.5

∑ f.x = (5 × 34.5) + (20 × 44.5) + (36× 54.5) + (16 × 64.5) + (10 × 74.5) + (4×84.5)

The sum of all frequencies: n = 5 + 20 + 36 + 16 + 10 + 4

= 91.

The formula for the standard deviation:

s=√n[(∑(f.x²)] - (∑(f.x))²/n(n-1)

s = √(91 × 922,926.5 - (4,905)²) / (91 × (91 - 1))

s =√((84,069,106.5 - 24,055,025) / (91 × 90))

s =85.63

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To prove that line segment a is parallel to line segment d, based on the given information, we can utilize the properties of perpendicular and parallel lines.

Given that a is perpendicular to b and b is perpendicular to c, we know that angles formed between a and b, as well as between b and c, are right angles. Let's denote these angles as ∠1 and ∠2, respectively.

Now, since c is parallel to d, we can conclude that the corresponding angles ∠2 and ∠3, formed between c and d, are congruent.Considering the fact that ∠2 is a right angle, it can be inferred that ∠3 is also a right angle.

By transitivity, if ∠1 is a right angle and ∠3 is a right angle, then ∠1 and ∠3 are congruent.Since corresponding angles are congruent, and ∠1 and ∠3 are congruent, we can deduce that line segment a is parallel to line segment d.

Thus, we have successfully proven that a is parallel to d based on the given information and the properties of perpendicular and parallel lines.

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Answer:

240 feet

Step-by-step explanation:

Given that,

The object falls 400 feet in 5 seconds.

We need to find how far it fall in 3 seconds.

5 seconds = 400 feet

1 second = 80 feet

So,

In 3 seconds,

d = (80×3) feet

= 240 feet

So, it will fall 240 feet in 3 seconds.

11/12

Answer:

1. find the least common denominator (LCD) of 2/3, 1/4 in other words, find the Least Common Multiple (LCM) of 3,4

Least Common Multiple (LCM) of 3,4 LCD = 12

Least Common Multiple (LCM) of 3,4 LCD = 122.

Least Common Multiple (LCM) of 3,4 LCD = 122.Make the Denominators the Same As The LCD.

Least Common Multiple (LCM) of 3,4 LCD = 122.Make the Denominators the Same As The LCD.2_x_4_ + _1 x 3__

Least Common Multiple (LCM) of 3,4 LCD = 122.Make the Denominators the Same As The LCD.2_x_4_ + _1 x 3__3 x 4 4x3

Least Common Multiple (LCM) of 3,4 LCD = 122.Make the Denominators the Same As The LCD.2_x_4_ + _1 x 3__3 x 4 4x33. Simplify denominators are Now The Same.

8/12 + 3/12

4. join the denominators

__8+3_____

12

5. Answer 11/12

Btw the Lines are Just For Separating numbers.

Answer:

60 different permutations of these letters can be made.

Step-by-step explanation:

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

\(P_{(n,x)} = \frac{n!}{(n-x)!}\)

How many different permutations of these letters can be made if no letter is used more than once?

3 letters from a set of 5. So

\(P_{(5,3)} = \frac{5!}{(5-3)!} = \frac{5!}{2!} = 5*4*3 = 60\)

60 different permutations of these letters can be made.

The percentile of 6.2 in the given data set is 40%.

To determine the percentile of 6.2 in the given data set, we can use the following steps:

Arrange the data set in ascending order:

4.2, 4.6, 5.1, 6.2, 6.3, 6.6, 6.7, 6.8, 7.1, 7.2

Count the number of data points that are less than or equal to 6.2. In this case, there are 4 data points that satisfy this condition: 4.2, 4.6, 5.1, and 6.2.

Calculate the percentile using the formula:

Percentile = (Number of data points less than or equal to the given value / Total number of data points) × 100

In this case, the percentile of 6.2 can be calculated as:

Percentile = (4 / 10) × 100 = 40%

The percentile of 6.2 in the sample data set is therefore 40%.

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Answer: 17/60 = 0.283333333333

25/60 = 0.416666666667

54/72 = 0.75

31/44 = 0.704545454545

Step-by-step explanation:

The piece-wise linear functions can be written as follows:

A linear function is modeled by:

y = mx + b

In which:

For x equal or less than -2, the line passes through (-3,-3) and (-2,-2), hence the rule is:

\(f(x) = x, x \leq -2\).

For x greater than -2 up to 1, the y-intercept is of -7, and the line also passes through (1,-8), hence the rule is:

\(f(x) = -x - 7, -2 < x \leq 1\).

For x greater than 1, the function goes through (2,-5) and (3,-3), hence the slope is:

m = (-3 - (-5))(3 - 2) = 2.

The rule is:

y = 2x + b.

When x = 2, y = -5, hence:

-5 = 2(2) + b

b = -9.

Hence:

\(f(x) = 2x - 9, x > 1\).

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Answer:

parallel: -1/4

perpendicular: 4

Step-by-step explanation:

so, the equation of your line iis y=-1/4x+1

for a line parallel to this line, the slope would have to be the same. therefore, the slope is -1/4.

however, in a line perpendicular to this line, the slope would have to be the opposite reciprocal. -1/4's opposite reciprocal is 4.

Answer:

Step-by-step explanation:

1. We know that a line that is parallel to another line will have no solutions, so the slopes have to be the same but the y-intercept needs to be different.

2. So, we would get y=-1/4x+4 for a parallel line.

3. For a line that is perpendicular to your line, there has to be one solution so that they intersect, so the slopes have to be different.

4. So, we would get y=-1/2x+1 for a perpendicular line.

I'm pretty sure this is correct, if it is wrong just please let me know and I'll remove it. Thank you.

Answer:(4,5π/4)

Step-by-step explanation:

Note that the point is on the circle whose radius is labeled 4, so r=4. The angle of the point is 5π4, so θ=5π4. Thus, the polar coordinates are (4,5π4).

We can see here that the type of quadrilaterals are:

22. Kite.

23. Parallelogram

24. Rhombus.

A quadrilateral is a shape with four sides, four vertices, and four angles that is only two dimensional. Convex and concave are the two main forms. Convex quadrilaterals can also be divided into a number of subgroups, including trapezoids, parallelograms, rectangles, rhombus, and squares.

We see that the first is kite because the adjacent sides are equal.

The second is a parallelogram because the opposite sides are congruent and the arrows point towards the slanted side of parallelogram.

Then the third is a rhombus because the diagonals bisect themselves and are equal. Also, they meet at 90°.

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Answer:

c

Step-by-step explanation:

log base 10 (5) is the expression

The value of the given expression can be written as log₁₀(5). which is the correct answer would be an option (C).

The logarithm of a number is often used in mathematics and science to simplify calculations and to solve equations involving exponential growth or decay.

In particular, the logarithm of a number is the exponent to which another fixed number, called the base, must be raised to produce that number.

As per the question, when you calculate the logarithm of 5 to base 10, written as log₁₀(5), you are finding the exponent to which 10 must be raised to produce the number 5.

Thus, the value of the given expression can be written as log₁₀(5).

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Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

0.288

Step-by-step explanation:

Given that :

Correlation (R) = 0.48

Slope of linear model which predicts Lifespan from years of education (m) = 0.8

To determine the value of slope of the model which predicts years of eductauoon from lifespan:

The square of the regression Coefficient is multiplied by the inverse of the slope of linear model which predicts Lifespan from years of education

Hence,

(R² * 1/m)

0.48² * 1/0.8

0.2304 * 1.25

= 0.288

Answer:

D. Quadrant IV

On the coordinate plane, you would go to the right two points, and then down 6, leading to quadrant IV

The solution to the nonlinear system of equations is (x, y) = (-3, -2) and (x, y) = (1, 6). These points represent the coordinates where the two equations intersect and satisfy both equations simultaneously.

To solve the nonlinear system of equations:

Equation 1: \(y = -x^2 + 7\)

Equation 2: y = 2x + 4

We can equate the right sides of both equations since they both represent y.

\(-x^2 + 7 = 2x + 4\)

To simplify the equation, we can rearrange it to be in the standard quadratic form:

\(x^2 + 2x - 3 = 0\)

Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. In this case, let's use factoring:

(x + 3)(x - 1) = 0

From this equation, we get two possible solutions:

x + 3 = 0 => x = -3

x - 1 = 0 => x = 1

Now, we substitute these x-values back into either equation to find the corresponding y-values.

For x = -3:

y = 2(-3) + 4

y = -6 + 4

y = -2

For x = 1:

y = 2(1) + 4

y = 2 + 4

y = 6

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Answer:

Domain:\(0 \le t \le 9\)

Range: \(7200 \ge \ d \ge \ 0\)

Step-by-step explanation:

Given

\(d = 7200 - 800t\)

Required

Determine the domain and range

From the attached graph, the values of t (on the horizontal axis) starts from 0 and ends at 9.

Hence, the domain is: \(0 \le t \le 9\)

When t = 0:

\(d = 7200 - 800t = 7200 - 800 * 0 = 7200\)

When t = 9

\(d = 7200 - 800t = 7200 - 800 * 9 = 0\)

Hence, the range is:

\(7200 \ge \ d \ge \ 0\)

Answer:

80π square feet

Step-by-step explanation:

The expression is 4 ₊ 12/x.

Given, the question says , four more than the quotient of 12 and a number x.

= 4 ₊ 12/x.

The outcome of dividing two numbers is the quotient.Three is the result of dividing six by two. In Latin, the word "quotient" implies "how many times." That makes a lot of sense since when you divide two numbers, you are calculating "how many times" the second number enters the first.

A term can be a number, a variable, the product of two or more variables, or the combination of a number and a variable. A single phrase or a collection of terms can make up an algebraic expression. For instance, 4x and y are the two terms in the formula 4x + y.

hence we framed the expression as 4 ₊ 12/x.

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Answer:

It would me shorter by about 31.4 inches

Step-by-step explanation:

Answer:

yes (longer)

Step-by-step explanation:

20π=62.83...

62.83...x10=628.31...

628.31.../12=52.35'

step one, finding circumference.

step two multiplying circumference by 10 pizzas

step three dividing 10x circumference by 12 inches to feet.