what is sum of squares formula

the ball will be traveling downward at a velocity of 24 feet per second after approximately 2.75 seconds.

What is velocity ?

Velocity can be defined as ratio of displacement and time taken.

To find the time when the ball will be traveling downward at a velocity of feet per second, we need to find the time when the velocity is equal to that value, which means the velocity is negative.

The velocity of the ball at any time t can be found by taking the derivative of the height function with respect to time:

v(t) = -32t + 64

We need to find the time t when v(t) = -24 feet per second. So we can set up the equation:

-32t + 64 = -24

Solving for t:

-32t = -88

t = 2.75 seconds (rounded to three decimal places)

Therefore, the ball will be traveling downward at a velocity of 24 feet per second after approximately 2.75 seconds.

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1. a. No, points A, C, and E are NOT coplanar.

This is because A and E are outside the plane)

b. The three lines are AE, CD, BC

c. The three collinear points are; A,B,E

d. The intersection of line AB and line CD is BE

A coplanar point is a point that lies in the same plane as one or more other points.

In three-dimensional space, a plane can be defined by at least three non-collinear points. Any additional point that lies on this plane is considered coplanar with those points.

In simpler terms, if you imagine a flat surface like a piece of paper, and you place some points on it, any additional point that you place on that same flat surface will be coplanar with the original points.

It's worth noting that coplanar points do not necessarily have to be in a straight line, as long as they all lie on the same plane.

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The value of f(-7) in the given function, f(x) = -x^2 + 2x + 6, is -57

From the question, we are to determine the value of f(-7) in the given function

The given function is

f(x) = -x^2 + 2x + 6

To find the value of f(-7) in the given function,

We will substitute -7 for x in the expression for f(x) and evaluate the resulting expression

That is,

f(x) = -x^2 + 2x + 6

f(-7) = -(-7)^2 + 2(-7) + 6

Simplifying this expression gives:

f(-7) = -49 - 14 + 6

f(-7)= -57

Hence, the value of f(-7) is -57

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The point on the curve y = x^2 - 3x + 5 where the normal is parallel to the tangent to the curve at the point (4, 9), we need to find the slope of the tangent at the point (4, 9) and then find the point on the curve where the slope of the normal is the same. The equation of the normal is y = -1/5x + 4.52.

First, find the derivative of the function y = x^2 - 3x + 5 to get the slope of the tangent:

dy/dx = 2x - 3

Next, plug in the x-value of the point (4, 9) to find the slope of the tangent at that point:

dy/dx = 2(4) - 3 = 5

The slope of the normal at any point on the curve will be the negative reciprocal of the slope of the tangent at that point. So, the slope of the normal at the point we are looking for will be -1/5.

To find the point on the curve where the slope of the normal is -1/5, set the derivative of the function equal to -1/5 and solve for x:

2x - 3 = -1/5

10x - 15 = -1

10x = 14

x = 1.4

Plug this x-value back into the original function to find the y-value:

y = (1.4)^2 - 3(1.4) + 5 = 4.24

So, the point on the curve where the normal is parallel to the tangent at the point (4, 9) is (1.4, 4.24).

Finally, to find the equation of the normal, use the point-slope form of a line:

y - y1 = m(x - x1)

y - 4.24 = -1/5(x - 1.4)

y = -1/5x + 4.52

So, the equation of the normal is y = -1/5x + 4.52.

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The illustration of 10 sided polygon is attached below.

Polygons are closed geometric figures made up of line segments that are connected end-to-end. The number of sides of a polygon determines the polygon's name.

In mathematical terms, a decagon is a 10-sided polygon with 10 vertices and 10 angles.

To draw a decagon, we need to start by drawing a circle. We can use a compass to draw a circle of any size we want. The radius of the circle will determine the size of the decagon.

Next, we need to draw a horizontal line through the center of the circle. This line will be the base of the decagon, and it will divide the circle into two equal halves.

Since a decagon has 10 sides, we need to divide the circle into 10 equal parts.

We can then use these lines as guides to draw the sides of the decagon. We start at one of the points where the lines intersect the circle, and draw a line segment to the next point.

We can label the vertices of the decagon with numbers, starting with 1 and going clockwise, as shown in the diagram.

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the shaded segment PQR will be 18.265m².

What is are of triangle?

The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.

The sum of all angle of triangle = 180

the diagram shows a sector OPQR of a circle, centre O and radius 8 cm.

Area of shaded part = Area of quadrant − Area of triangle

=πr²/ 4 - 1/2 bh

= π × 8²/ 4  - 1/ 2 × 8× 8

= 18.265m².

Hence the shaded segment PQR will be 18.265m².

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There are 2 tablespoons in 1 fluid ounce. This conversion is often used in cooking and baking recipes, where ingredients are measured in ounces or tablespoons.

Fluid ounces and tablespoons are both units of volume used to measure liquids in cooking and baking recipes. One fluid ounce is equal to 29.5735 milliliters or approximately 2 tablespoons, which is equivalent to 6 teaspoons. Therefore, there are 2 tablespoons in 1 fluid ounce.

This conversion is important to know when following recipes that call for ingredients in fluid ounces or tablespoons. It allows for accurate measurement of ingredients, which is crucial for successful cooking and baking. Other common units of volume used in the kitchen include teaspoons, cups, and quarts, among others.

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The total number of pages in Rhett's book is 183 pages.

A solution to an equation is a number that can be substituted for the variable to provide a piece of true number information.

To determine the total number of pages in Rhett's book, we need to solve for p in the equation:

p + 31 = 214

First, we can separate p on one side of the equation by subtracting 31 from both sides:

p + 31 - 31 = 214 - 31

Simplifying:

p = 183

Therefore, the total number of pages in Rhett's book is 183 pages.

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Answer:

24

Step-by-step explanation:

Formula is number of possibilities = n (n-1) (n-2) ....1

Here, n = 4

So, number of possibilities = 4 x 3 x 2 x 1 = 24

You can also use following method to count:

ABCD

ABDC

ACBD

ACDB

ADBC

ADCB

--------

BACD

BADC

BCAD

BCDA

BDAC

BDCA

---------

CABD

CADB

CBAD

CBDA

CDAB

CDBA

--------

DABC

DACB

DBAC

DBCA

DCAB

DCBA

--------

Total 24 combinations

The given statement is false.

You can compare two marginal distributions to see if the corresponding two variables are related - False.

Comparing marginal distributions can only disclose information about the distribution of each variable individually, not whether the variables are connected or not.

To see if two variables are connected, we must look at their joint distribution or conditional distribution. To examine the degree and direction of a link between two variables, statistical approaches such as correlation analysis or regression analysis can be utilised.

As a result, comparing marginal distributions is insufficient to tell whether two variables are connected or not.

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To multiply mixed numbers, convert to improper fractions, cancel factors, multiply the remaining factors, and simplify if possible.

Increasing blended numbers can be tedious, yet there is an easy route that can work on the interaction. To duplicate blended numbers, convert them to ill-advised portions, then drop any elements that show up in both the numerator and denominator of the divisions. At long last, duplicate the leftover elements in the numerator and denominator and work on the subsequent division if conceivable. For instance, to duplicate 2 1/2 by 3 2/3, first proselyte them to inappropriate divisions, which are 5/2 and 11/3. Then, drop the variable of 2 in the numerator of the principal portion and the denominator of the subsequent division. The outcome is 55/3, which can be improved to 18 1/3. This alternate way can save time and assist understudies with taking care of augmentation issues all the more proficiently.

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Standard conversions state that 375 cm is equivalent to 147.6 inches.

A fixed magnitude of a quantity that serves as a reference point for measuring other quantities of the same sort is referred to as a unit of measurement. Convention or legislation establish and adopt it. Every other amount of that sort can be expressed as a multiple of the unit of measurement.

One inch is 2.54 cm long.

We can compose,

2.54 cm equals one inch.

1 cm equals 0.54"

Thus, 375 cm will be equal to 375/2.54 inch.

175 cm = 147.6 in.

So, 375 cm equals 147.6 inches in inches.

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Complete question - what is 375cm in inches?

The expression can be written as ⁴√y. The solution has been obtained by solving the radical expressions.

What are radical expressions?

A square root-containing expression is referred to as a radical expression. When a root other than a square root is being represented, the radical sign's 'V'-shaped component will have a superscript number.

We are given expression as y to the three fourths power, all over y to the one half power. This can be written as

[tex]\frac{y^{3/4}}{y^{1/2} }[/tex]

We know that

cᵃ ÷ cᵇ = cᵃ⁻ᵇ

So, using this we get

[tex]y^{3/4 - 1/2[/tex]

[tex]y^{1/4[/tex]

Since, we have to represent this in the radical form, we know that

b[tex]^{1/a}[/tex] = ᵃ√b

So, using this we get

[tex]y^{1/4[/tex] = ⁴√y

Hence, the expression can be written as ⁴√y.

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The bucket of fish are the sea otters fed each day is 2 buckets or 3/2 bucket(in fractions).

What is fraction?
A fraction is a mathematical expression that represents a part of a whole. It is written as a number (the numerator) over another number (the denominator), separated by a horizontal line. The denominator indicates the number of equal parts into which the whole is divided, while the numerator indicates how many of those parts are being considered.

Explanation:

The sea otters are fed 1/4 as much fish as the dolphins, which means they are fed:

(1/4) x 6 = 6/4 = 3/2 buckets of fish each day.

However, we cannot have half a bucket of fish, so we need to round this up to the nearest whole number. Therefore, the sea otters are fed:

2 buckets of fish each day.

So the answer is: 2 buckets.

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In general, whether or not an individual needs to file a tax return depends on a number of factors, including income, filing status, and age.

In the United States, for example, the IRS sets income thresholds each year, and individuals whose income exceeds these thresholds are generally required to file a tax return.

However, there are many exemptions and exceptions to this general rule, and individuals should consult the IRS website or a tax professional for more information specific to their situation.

Other countries may have different rules and requirements for filing tax returns, so it's important to check with the tax authority in your own country for specific guidance.

P.S Your question is incomplete, so I gave you a general overview to help you better understand filing tax returns.

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The difference between the two pots is 4731.761 cm^3

How to determine this?

1 gallon = 3785.41 cm^3

2 gallons = 3785.41 cm^3 *2

= 7570.82 cm^3

And also,

1 quart = 946.353 cm^3

3 quarts = 946.353 cm^3 * 3

= 2839.059 cm^3

So, the difference between the two

= 7570.82 cm^3 - 2839.059 cm^3

= 4731.761 cm^3

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The Taylor series for sin(x) is an infinite series expansion that represents the trigonometric function sin(x) as a sum of infinite terms involving the powers of x.

The Taylor series for sin(x) can be written as:

where n! represents the factorial of n.

The series converges for all values of x, which means that it can be used to calculate the value of sin(x) to any desired degree of accuracy. The series is based on the idea that any continuous function can be represented as an infinite sum of terms involving the function's derivatives at a particular point, in this case, x=0.

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Answer:whitch one are they talking about I think it might be answer 3

Step-by-step explanation:

The five steps to solving an inequality are as follows:

1.Identify the inequality - In the equation, the inequality symbol should be identified first.

2.Isolate the variable - The inequality should be rearranged so that the variable is on one side, and all other terms are on the other side.

3.Simplify the inequality - Multiplication and division rules should be used to simplify the equation.

4.Solve the inequality - The simplified inequality can be solved for the variable.

5.Graph the solution - The solution should be graphed on a number line in order to visualize it.

In summary, solving an inequality requires the identification of the inequality symbol, the isolation of the variable, the simplification of the inequality, the solving of the inequality, and the graphing of the solution. Following these steps carefully will ensure that the inequality is solved accurately.

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Answer:

here is how to solve the math problems with sales tax and discount:

a) To find the total bill, we need to add the purchase price and the sales tax. To find the sales tax, we need to multiply the purchase price by the sales tax rate. The purchase price is the sum of the prices of the two pairs of shoes, which is $37 + $42 = $79. The sales tax rate is 7%, which as a decimal is 0.07. So, the sales tax is 0.07 x 79 = $5.53. The total bill is 79 + 5.53 = $84.53.

b) To find the discounted price, we need to subtract the discount from the original price. To find the discount, we need to multiply the original price by the discount rate. The original price is the same as the purchase price in part a, which is $79. The discount rate is 25%, which as a decimal is 0.25. So, the discount is 0.25 x 79 = $19.75. The discounted price is 79 - 19.75 = $59.25. To find the total bill with the coupon, we need to add the sales tax to the discounted price. The sales tax rate is still 7%, which as a decimal is 0.07. So, the sales tax is 0.07 x 59.25 = $4.15. The total bill with the coupon is 59.25 + 4.15 = $63.40.

I hope this helps!

Step-by-step explanation:

The fraction of the height of Cleopatra's clock that is the height of Ptolemy's clock is 2/5

A fraction is a mathematical concept that represents a part of a whole or a ratio between two quantities. It is typically written in the form of a numerator over a denominator, separated by a horizontal line, such as 1/2, 3/4, or 7/8.

Given that the volume of cylinder = πr^2h

Let's denote the height and radius of Cleopatra's water clock as h_c and r_c, respectively, and the height and radius of Ptolemy's water clock as h_p and r_p, respectively.

Since both clocks drain uniformly, we can use the formula for the volume of a cylinder to relate the height and radius of each clock to the time it takes to drain:

Volume of Cleopatra's clock = [tex]\pi r^2_ch_c[/tex]

Volume of Ptolemy's clock = [tex]\pi r^2_ph_p[/tex]

Since Cleopatra's clock drains in 4 hours, the rate of draining is (Volume of Cleopatra's clock) / (4 hours), and similarly for Ptolemy's clock.

We are given that after 2 hours of draining, both clocks have the same water height.

Therefore, we can set the two rates of draining equal to each other and solve for the ratio of heights:

(Volume of Cleopatra's clock) / (4 hours) = (Volume of Ptolemy's clock) / (5 hours)

hc/hp = [tex](r_p/r_c)^2 * (5/4)[/tex]

After two hours of draining, the water height in both clocks is the same, so we can set the volume of water in each clock equal to each other:

[tex]r^2_ch_c/2 = r^2_ph_p[/tex]

Now, we can solve for the ratio of water heights after each clock has been draining for three hours:

Water height in Cleopatra's clock after 3 hours = [tex]h_c - (3/4)h_c = (1/4)h_c[/tex]

Water height in Ptolemy's clock after 3 hours = [tex]h_p - (3/5)h_p = (2/5)h_p[/tex]

hp= 1/10

Therefore, the fraction of the height of Cleopatra's clock that is the height of Ptolemy's clock is:

hp/hc = 1/10/(1/4) = 2/5

And the fraction of the water height of Ptolemy's clock that is equal to the water height of Cleopatra's clock after each has been draining for three hours is:

hc/(2/5)hp = (1/4)/(2/5)(1/10)

= 5/4.

Hence,

The fraction of the height of Cleopatra's clock that is the height of Ptolemy's clock is: 2/5

The fraction of the water height of Ptolemy's clock that is equal to the water height of Cleopatra's clock after each has been drained for three hours is: 5/4.

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Answer:

114.3

Step-by-step explanation:

multiple the length value by 2.54

Answer:

Answer: The length of the path would be 35 yds.

Step-by-step explanation:

We can use the formula for the area of a right triangle to find the length of the other leg. Once we know the lengths of both legs, we can use the Pythagorean theorem to find the length of the hypotenuse.

Let's call the length of the shortest side (the leg) "a", and let's call the length of the other side (the other leg) "b". We know that a = 21 yd and the area of the triangle is 294 yd^2. So we can use the formula for the area of a right triangle to solve for b:

area = (1/2) * a * b

294 = (1/2) * 21 * b

b = (2 * 294) / 21

b = 28

Now we know that a = 21 yd and b = 28 yd. We can use the Pythagorean theorem to find the length of the hypotenuse (c):

c^2 = a^2 + b^2

c^2 = 21^2 + 28^2

c^2 = 441 + 784

c^2 = 1225

c = sqrt(1225)

c = 35

Therefore, the length of the path along the longest side of the playground would be 35 yds.

Answer:

35 yards.

Step-by-step explanation:

We can use the Pythagorean theorem to solve this problem. Let's call the other leg of the triangle "x" and the length of the hypotenuse (the path the council would like to add) "c". Then we have:

Area of triangle = (1/2) * base * height

294 = (1/2) * 21 * x

x = 28

Now we can use the Pythagorean theorem to find "c":

c^2 = 21^2 + 28^2

c^2 = 441 + 784

c^2 = 1225

c = sqrt(1225)

c = 35

So the length of the path the council would like to add is 35 yards.

Answer:

[tex] \sf \: d) \: 6[/tex]

Step-by-step explanation:

Now we have to,

→ Find the required value of x.

The equation is,

→ 2x + 12 = 24

Then the value of x will be,

→ 2x + 12 = 24

→ 2x = 24 - 12

→ 2x = 12

→ x = 12 ÷ 2

→ [ x = 6 ]

Hence, option (d) is correct.

There are 0.625 (or approximately 5/8) gallons in 80 fluid ounces. It's worth noting that the conversion factor between fluid ounces and gallons can vary depending on the system of measurement used

There are 128 fluid ounces in a gallon in the US customary system of measurement. Therefore, to find out how many 80-ounce containers are in a gallon, you can use the following formula:

number of 80-ounce containers in a gallon = 128 / 80

Simplifying this expression, we can perform the division:

number of 80-ounce containers in a gallon = 1.6

This means that there are 1.6 (or approximately 1 and 3/5) 80-ounce containers in a gallon.

Alternatively, you can convert the 80 ounces to gallons using the following formula:

number of gallons in 80 fluid ounces = 80 / 128

Again, simplifying this expression, we can perform the division:

number of gallons in 80 fluid ounces = 0.625

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The closed shapes with four sides are called quadrilaterals.

Therefore, the four sides closed shape is known as quadrilateral.

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Hello!

Answer:

A. The theoretical probability of flipping 3 heads on one flip of three coins is (1/2) * (1/2) * (1/2) = 1/8. Since you flipped three heads 7 times out of 50, the experimental probability of flipping 3 heads is 7/50.

B. To calculate the theoretical probability of flipping less than 3 heads, we can calculate the probability of flipping 0, 1, or 2 heads and add them together. The probability of flipping 0 heads is (1/2) * (1/2) * (1/2) = 1/8, since all three coins must come up tails. The probability of flipping 1 head is (1/2) * (1/2) * (1/2) * 3 = 3/8, since there are three ways to get one head (HTT, THT, TTH). The probability of flipping 2 heads is (1/2) * (1/2) * (1/2) * 3 = 3/8, since there are three ways to get two heads (HHT, HTH, THH). Therefore, the theoretical probability of flipping less than 3 heads is:

1/8 + 3/8 + 3/8 = 7/8.

So the theoretical probability of flipping less than 3 heads is 7/8.

The conversion of 185 centimetres in feet is equals to the 6.06 feet. Thus, conversion factor from centimetres to feet is 6.06/185 = 0.032.

A conversion factor is a number used to convert one set of units into another set of units by multiplication or division. If conversion is necessary, a conversion factor suitable for equivalent value must be used. For example, to convert meters to centimetres, the appropriate conversion value is 100 centimetres equal 1 meter. It includes converting a value from inches to millimeters, for distance from miles to kilometers, feet or other units. How to convert centimeters to feet : One meter is a measure of length and equals approximately 3.28 feet. Thus conversion factor is 3.28 feet. So,185 meters

= 185 × 3.28 feet

= 606.8 feet --(1)

But we need to convert 185 centimeters to feet. So, change meters to centimeters. As you know, 1 meter = 100 centimeters, so 185 meters = 18500 centimeters --(2). Now from equations (1) and (2),

18500 centimeters = 606.8 feet,

Divide both parts by 100,

=> 185 centimetres = (606.8/100 ) feet

= 6.06 feet

Hence required value is 6.06 ft.

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Answer:

they’re both negative to -4.5 is the answer

Step-by-step explanation:

Answer: They’re both negative to -4.5 is the answer

Step-by-step explanation:

To find the axis of reflection for a given object or shape, follow these steps:

1. On a coordinate plane, draw the shape or object. You can do this with graph paper or a computer programme.

2. Find the reflection point or line. This will be the reflection axis. A line that divides a shape or object into two mirror images is referred to as the axis of reflection.

3. Determine the axis of reflection equation. If the axis of reflection is a straight line, the equation is x = a, where an is a constant. If the reflection axis is a horizontal line, the equation will be y = b, where b is a constant.

4. Reflect the shape or object across the axis of reflection to check your work. To accomplish this, flip the shape or object across the axis of reflection and ensure that it appears identical to the original shape or object.

You can also use an online axis of reflection calculator to find the axis of reflection for a given shape or object. To find an axis of reflection calculator, simply type "axis of reflection calculator" into your preferred search engine and select one of the results.

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