What is the graph of a quadratic equation known as?

The arc length of the curve y = (1/3)x^(3/2) on [0,60] is approximately 137.78 units.

For the arc length of the curve y = (1/3)x^(3/2) on [0,60], we can use the formula:

L = ∫[a,b] √(1 + [f'(x)]²) dx

where f(x) = (1/3)x^(3/2) and a = 0, b = 60.

We first need to find f'(x):

f'(x) = d/dx [(1/3)x^(3/2)] = (1/2)x^(1/2)

Now we can plug this into the formula:

L = ∫[0,60] √(1 + [(1/2)x^(1/2)]^2) dx

 = ∫[0,60] √(1 + (1/4)x) dx

To evaluate this integral, we can use the substitution u = 1 + (1/4)x, du/dx = 1/4, which gives us:

L = 4 ∫[1/4,16] √u du

 = (8/3) [u^(3/2)] [1/4,16]

 = (8/3) [(16^(3/2) - (1/4)^(3/2))]

 ≈ 137.78

Therefore, the arc length of the curve y = (1/3)x^(3/2) on [0,60] is approximately 137.78 units.

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The equation which represent the proportional relationship between the number of pairs of socks that Martha buys, x, and the total cost (in dollars), y is y = bx

y = bx

Where,

b = constant

If y = $6 and x = 2 pairs

y = bx

6 = b × 2

6 = 2b

divide both sides by 2

b = 6/2

b = 3

In conclusion, the proportional relationship between number of pairs of socks that Martha buys, x, and the total cost (in dollars), y is y = bx

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Answer:

b.  20°

Step-by-step explanation:

Find the missing angle in the top triangle:

180 - 40 - 20 = 120

because, the sum of interior angles of a triangle is 180.

The top angle of the bottom triangle = 120 because it is a vertical angle to the one you just found.

Now find the missing angle (x) on the bottom:

x = 180 - 120 - 40 = 20

Answer:

The slope is 3/2, and the y-intercept (b) is -1

Step-by-step explanation:

The slope-intercept form is y=mx+b. m is the slope and b is the y-intercept.

Answer:

Yes

Step-by-step explanation:

Yes because if you insert -39 for x and 42 for y then your equation is:

42 = -39 + 81

If you were to solve this equation it would be true.

The area of a rectangle is the product of its length and breadth. The maximum area enclosed by the fence is 36800 square meter  and the dimensions of the enclosed area are 115 meter and 320 meter.

A rectangle is a type of parallelogram having equal diagonals.

All the interior angles of a rectangle are equal to the right angle.

The diagonals of a rectangle do not bisect each other.

The dimensions of the given rectangle is (650 - 2x) and x.

Then, the area of the given rectangle is A(x)  = x(650 - 2x)

In order to find the maximum area enclosed take the derivative of A(x) and equate it to zero as follows,

(660 - 2x) - 2x = 0

=> 4x = 660

=> x = 660 / 4

=> x = 115

Now, the maximum area is the value of A(x) at x = 115 as below,

= 115 × (650 - 2×115)

= 115 × 320

= 36800

The dimensions for the maximum area are 115 and (650 - 2 × 115) = 320.

Hence, the largest area enclosed is 36800 square meter and the dimensions of the enclosed area are 115 meter and 320 meter.

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Answer:“To get the average rate of change between 2 points...” To get the average rate of change between 2 points, plug in their coordinate values into the equation (y2-y1)/(x2-x1). The values come from the points (x1,y1) and (x2,y2).

Step-by-step explanation:

Answer:

A rational number is a number such as -3/7 that can be expressed as the quotient or fraction a/b of two integers, a numerator q and a non-zero denominator b. Every integer is a rational number: for example, 10 = 10/1.

No.

\(5 \frac{1}{3} \)

So we can turn from 5 1/3 to 16/3

Note that 16/3 makes infinity decimal but if the infinity decimal can be turnt into a fraction, it will be classified as rational number.

Answer:

There are \(5\) five dollar bills and \(4\) ten dollar bills.

Step-by-step explanation:

Given:

Selling price of bicycle \(=\$65\).

The friend gave \(x\) five dollar bills and \(y\) ten dollar bills.

Total number of bills \(=9\).

To find: Number of five dollar bills and ten dollar bills the friend gave.

Solution:

The friend gave \(x\) five dollar bills and \(y\) ten dollar bills and the friend gave \(9\)bills in all.

So, \(x+y=9\).

\(\Rightarrow x=9-y ...(i)\)

Selling price of bicycle \(=\$65\).

So, \(5x+10y=65...(ii)\)

Putting the value of \(x\) from equation \((i)\) in equation \((ii)\).

\(\Rightarrow 5(9-y)+10y=65\)

\(\Rightarrow 45-5y+10y=65\)

\(\Rightarrow 45+5y=65\)

\(\Rightarrow 5y=65-45\)

\(\Rightarrow 5y=20\)

\(\Rightarrow y=\frac{20}{5}\)

\(\Rightarrow y=4\)

Now, putting the value of \(y\) in equation \((i)\).

\(\Rightarrow x=9-4\)

\(\Rightarrow x=5\)

Hence, there are \(5\) five dollar bills and \(4\) ten dollar bills.

The proportion of population having score between 65 to 110 is 81.85%.

We have-

Mean of population = 80

Standard deviation of population = 15

We are supposed to find the proportion of the population corresponding to scores between 65 and 110.

According to the formula of the Z-score.

z = (x-μ)/σ

X=interval, μ= population mean ,

σ= standard deviation

Here,x = 65,μ= 80,σ= 15 andz = (65-80)/15z = -1

For Z=-1, From the z-table, the area to the left is 0.1587

Now, we need to find the area in the right  It can be calculated as follows.

z = (110-80)/15 = 2.

Area to the left of Z=2.00 is 0.028

So, the area between Z= -1 and Z= 2 is

= Total Area - (area of population below 65 + area of population above 110)=1-(0.1587+0.0228)=0.8185

The proportion of the population corresponding to scores between 65 and 110 is 0.8185 or 81.85%.

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In the equation f(x) = (x - h)² + k, the value of k represents the vertical shift of the graph, indicating the y-coordinate of the new vertex.

To determine the value of k in the equation f(x) = (x - h)² + k, we need to consider the transformation of the original function f(x) = x².

Comparing the two equations, we observe that the transformation involves shifting the graph horizontally by h units and vertically by k units.

In the original function f(x) = x², the vertex of the parabola is located at the point (0, 0), which means k is 0.

However, when the equation is rewritten in the form f(x) = (x - h)² + k, the vertex is shifted to the point (h, k).

Since the original vertex is (0, 0) and the new vertex is (h, k), it implies that k is the y-coordinate of the new vertex.

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The toroid formed by rotating the rectangular figure gives;

a. A toroid

b. 374•π

c. 400•π

d. The surface area will be 4 times the initial surface area

The volume will be 8 times the initial volume

Taking the distance from the y-axis as 8

Width of the rectangle; 2.5

Length; 6

We have;

a. The solid of revolution is a toroid, having sharp corner edges

b. The surface area is found using the surface area of a hollow cylinder as follows;

Outer radius = 8 + 6 = 14

Inside radius = 8

Width = 2.5

Outer area = 2• π × 14 × 2.5 = 70•π

Inner area = 2• π × 8 × 2.5 = 40•π

\({\pi \cdot 14 }^{2} - {\pi \cdot 8 }^{2} = 132 \cdot\pi\)

The surface area of the figure is therefore;

c. The volume of the solid of revolution is found as follows;

\({\pi \cdot 14 }^{2} \times 2.5 - {\pi \cdot 8 }^{2} \times 2.5= 400 \cdot \pi\)

e. When the dimensions are doubled, we have;

The linear scale factor = 2

The area scale factor = 2^2 = 4

Therefore;

The volume scale factor = 2^3 = 8

The volume of the solid following the enlargement, is therefore;

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Answer:

Step-by-step explanation:

Divide

the cosine and the sine to get the tangent.

Answer:

2.65909090

Step-by-step explanation:

tangent of an angle can be defined in terms of the cosine and sine value of the angle such that: \(tan(\theta)=\frac{sin(\theta)}{cos(\theta)}\), this can be used to explain why tan(theta) is undefined at some angles, which is just when cos(theta) = 0.

Anyways, we can plug in the values of cosine and sine to get:

\(tan(a) = \frac{0.936}{0.352}\)

Divide:

\(tan(a) = 2.65\overline{90}\)

The mode is the value that appears most frequently in a dataset. In this case, the mode is 4, as it has the highest frequency of occurrence.

The median is the middle value when the data is arranged in ascending or descending order. Since there are an odd number of families (21 in total), the median will be the value of the 11th observation when the data is sorted. Arranging the data in ascending order, we find that the median is also 4, as it is the middle value.

The mean is the average value and is calculated by summing up all the values and dividing by the total number of observations. In this case, we can calculate the mean by multiplying each number of pets by its corresponding frequency, summing up these products, and dividing by the total number of families (21). Using this approach, the mean can be calculated as:

Mean = (0*2 + 1*1 + 2*8 + 3*1 + 4*9 + 5*0) / 21 ≈ 2.76

Therefore, based on the provided data, the mode, median, and mean number of pets owned by the families are all approximately 4.

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Answer:

c is the answer

Step-by-step explanation:

just a guess

Answer:

i think its either a or c, but my best guess is c

Step-by-step explanation:

If the null hypothesis is rejected, it suggests that there is evidence to support the claim that the mean weight of Take-a-Bite snack food is less than 175 grams.

What is the standard deviation?

The standard deviation is a measure of the dispersion or variability of a set of data points. It quantifies how much the individual data points deviate from the mean of the data set.

To test the claim that the mean weight of Take-a-Bite snack food is less than 175 grams, we can conduct a one-sample t-test. Here's how we can perform the test at a significance level of 0.05:

Step 1: State the null and alternative hypotheses:

Null Hypothesis (H0): The mean weight of Take-a-Bite snack food is equal to 175 grams.

Alternative Hypothesis (H1):

The mean weight of Take-a-Bite snack food is less than 175 grams.

Step 2: Determine the test statistic:

Since the population standard deviation is unknown, we use the t-test statistic. The test statistic for a one-sample t-test is calculated as: t = (sample mean - hypothesized mean) / (sample standard deviation / √n)

In this case, the sample mean is 172 grams, the hypothesized mean is 175 grams, the sample standard deviation is 8 grams, and the sample size is 70.

Step 3: Set the significance level: The significance level (alpha) is given as 0.05.

Step 4: Calculate the test statistic:

t = (172 - 175) / (8 / √70) ≈ -1.158

Step 5: Determine the critical value and p-value:

Since we are conducting a one-tailed test to check if the mean weight is less than 175 grams, we need to find the critical value or p-value for the lower tail.

Using a t-distribution table or statistical software, we can find the critical value or p-value associated with a t-statistic of -1.158 and degrees of freedom (df) equal to n - 1 (70 - 1 = 69) at a significance level of 0.05.

Step 6: Make a decision:

If the p-value is less than the significance level (0.05), we reject the null hypothesis. If the critical value is greater than the test statistic, we reject the null hypothesis.

Step 7: Interpret the results:

Based on the calculated test statistic and critical value or p-value, make a conclusion about the null hypothesis. If the null hypothesis is rejected, it suggests that there is evidence to support the claim that the mean weight of Take-a-Bite snack food is less than 175 grams. If the null hypothesis is not rejected, there is insufficient evidence to support the claim.

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Answer:

The answer is D

Step-by-step explanation:

Option D will be the answer.

  Given in the question,

Steps to calculate the Dew point temperature,

If the original temperature is 35°C,

Step 1,

Subtract 20°C → (35°- 20°) = 15°

Step 2,

Add 1° foe every 5 points,

Hence, Dew point temperature = \(15^\circ+\frac{1}{5}R\)

If the dew point is 30°C, expression will be,

\(30^\circ=15^\circ+\frac{1}{5}R\)

  Therefore, Option D will be the answer.

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Answer:

broke

Step-by-step explanation:

----$$$$$$$

Using implicit differentiation, The equation of the tangent line to the curve at (1, 2) is: y = (-1/3)x + (7/3)

For the curve sin(x+y) = 2x-2y at the point (pi, pi):

Taking the derivative of both sides with respect to x using the chain rule, we get:

cos(x+y) (1 + dy/dx) = 2 - 2dy/dx

Simplifying, we get:

dy/dx = (2 - cos(x+y)) / (2 + cos(x+y))

At the point (pi, pi), we have x = pi and y = pi, so cos(x+y) = cos(2pi) = 1.

Therefore, the slope of the tangent line at (pi, pi) is:

dy/dx = (2 - cos(x+y)) / (2 + cos(x+y)) = (2 - 1) / (2 + 1) = 1/3

Using the point-slope form of the equation of a line, the equation of the tangent line at (pi, pi) is:

y - pi = (1/3)(x - pi)

Simplifying, we get:

y = (1/3)x + (2/3)pi

For the hyperbola x^2 + 2xy - y^2 + x = 2 at the point (1, 2):

Taking the derivative of both sides with respect to x using the product rule, we get:

2x + 2y + 2xdy/dx + 1 = 0

Solving for dy/dx, we get:

dy/dx = (-x - y - 1) / (2x + 2y)

At the point (1, 2), we have x = 1 and y = 2, so the slope of the tangent line at (1, 2) is:

dy/dx = (-x - y - 1) / (2x + 2y) = (-1-2-1)/(2+4) = -2/6 = -1/3

Using the point-slope form of the equation of a line, the equation of the tangent line at (1, 2) is:

y - 2 = (-1/3)(x - 1)

Simplifying, we get:

y = (-1/3)x + (7/3)

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Answer:

and this is why I do not like math also all u got to do is count all the squares and the corners do not count as wholes u got to put two together and then it makes a whole

Step-by-step explanation:

its just that easy  :D hope it was helpful

The average speed of the ball which travelled 24 meters in 8 seconds is 3m/s.

Speed is simply referred to as distance traveled per unit time.

Mathematically, Speed = Distance ÷ time.

Given the data in the question;

To determine the average speed of the ball, plug the given values into the above equation and simplify.

Speed = Distance / time

Speed = 24 meters / 8 seconds

Speed = 3m/s

Therefore, the speed is 3 meters per seconds.

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(a)The range of the given set of measurements is 4.

(b)The sample mean of the given set of measurements is approximately 5.625.

(c)The sample variance of the given set of measurements is approximately 2.337768, and the sample standard deviation is approximately 1.529.

(a) The range is the difference between the largest and smallest values in the set of measurements. In this case, the largest value is 8 and the smallest value is 4, so the range is 8 - 4 = 4.

To calculate the range, we subtract the smallest value from the largest value. In this case, the largest value is 8 and the smallest value is 4.

Range = Largest value - Smallest value

Range = 8 - 4

Range = 4

The range provides a simple measure of the spread or dispersion of the data. In this case, the range tells us that the values range from the smallest value of 4 to the largest value of 8, with a difference of 4 between them.

(b) The sample mean, denoted as x, is the sum of all the measurements divided by the total number of measurements.

To calculate the sample mean, we add up all the measurements and then divide by the total number of measurements. In this case, we have 8 measurements.

Sum of measurements = 4 + 4 + 7 + 6 + 4 + 6 + 6 + 8 = 45

Sample mean = Sum of measurements / Total number of measurements

Sample mean = 45 / 8

Sample mean ≈ 5.625

The sample mean represents the average value of the measurements and provides a measure of central tendency.

(c) The sample variance, denoted as s^2, measures the variability or dispersion of the data points around the sample mean. It is calculated as the average of the squared differences between each measurement and the sample mean.

To calculate the sample variance, we first calculate the squared difference between each measurement and the sample mean. Then, we average those squared differences.

Squared difference for each measurement:

(4 - 5.625)^2 = 2.890625

(4 - 5.625)^2 = 2.890625

(7 - 5.625)^2 = 1.890625

(6 - 5.625)^2 = 0.140625

(4 - 5.625)^2 = 2.890625

(6 - 5.625)^2 = 0.140625

(6 - 5.625)^2 = 0.140625

(8 - 5.625)^2 = 5.390625

Sum of squared differences = 2.890625 + 2.890625 + 1.890625 + 0.140625 + 2.890625 + 0.140625 + 0.140625 + 5.390625 = 16.364375

Sample variance = Sum of squared differences / (Total number of measurements - 1)

Sample variance = 16.364375 / (8 - 1)

Sample variance ≈ 2.337768

The standard deviation, denoted as s, is the square root of the sample variance.

Sample standard deviation = √(Sample variance)

Sample standard deviation = √(2.337768)

Sample standard deviation ≈ 1.529

These measures provide information about the dispersion or spread of the data points around the sample mean. A higher variance or standard deviation indicates greater variability in the measurements.

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In this scenario, we are given the following information: sample size (n) is 49, sample mean (P) is 50, sample standard deviation (s) is 7, null hypothesis (H₀) states that the population mean (μ) is greater than or equal to 52, and the alternative hypothesis (Hₐ) states that the population mean is less than 52.

The test statistic for this situation is the t-statistic, which measures the difference between the sample mean and the hypothesized population mean, taking into account the sample size and the sample standard deviation. It is used to assess the evidence against the null hypothesis. In this case, since the alternative hypothesis states that the population mean is less than 52, we have a left-tailed test. To calculate the t-statistic, we use the formula:

t = (P - μ) / (s / √n)

Plugging in the given values:

t = (50 - 52) / (7 / √49) = -2 / (7 / 7) = -2

Therefore, the test statistic for the provided information is -2. This value represents the standardized difference between the sample mean and the hypothesized population mean, accounting for the sample size and standard deviation. It indicates that the sample mean is 2 standard deviations below the hypothesized population mean of 52.

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An isosceles triangle is one with two equal-length sides. The value of l is 8 ft.

An isosceles triangle is one with two equal-length sides. It is sometimes stated as having exactly two equal-length sides, and sometimes as having at least two equal-length sides, with the latter form containing the equilateral triangle as a particular case.

In the given image it can be observed except 140° angle, the other two angles are congruent to each other which means the triangle is an isosceles triangle.

As per the base angle theorem in an isosceles triangle the sides opposite to the congruent triangle are equal therefore, the length of side l will be 8 ft as well.

Hence, the value of l is 8 ft.

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Answer:

the answer is

x-2=48

r-8= -12

Answer:

7

Step-by-step explanation:

-4d+3

-4(-1) + 3   Insert -1 for d

4+3=7

ANSWER :

The downpayment is $35,000

EXPLANATION :

The house is $175,000 and the downpayment is 20%

To get the amount of downpayment, multiply 20% or 0.20 by the amount of the house.

That will be :

Answer:

$1,738.95

Step-by-step explanation:

FV = PV(1+r/n)^nt

FV = future value

PV = present value = $1,500

r = interest rate = 3.0% = 0.03

n = Number of periods = 1

t = 5 years

FV = PV(1+r/n)^nt

= 1,500(1 + 0.03/1)^1*5

= 1,500(1 + 0.03)^5

= 1500(1.03)^5

= 1,500(1.1593)

= 1,738.95

FV = $1,738.95

The future value of your deposit after 5 years is $1,738.95

Answer:

7 < x < 11

Step-by-step explanation: