The senior class want to play a practical joke on the principal, who was a former college basketball star. They want to fill his office full of basketballs. The diameter of a basket ball is 9.5 inches. The dimensions for his office are 20 feet long, 18 feet wide and 12 feet tall. If you assume there is not furniture in the office, then approximately how many basketballs would it take to fill up his entire office to the ceiling? (Model the basketball as a sphere).

Answer:

=-1.66

Step-by-step explanation:

Answer: See explanation

Step-by-step explanation:

a) A large pizza with one topping costs $15.50. A large pizza with 4 toppings costs $20.

A large pizza with one topping costs $15.50.

Using the formula for direct variation,

y = kx

where,

y = Cost of pizza

x = number of toppings

k = constant of proportionality

15.50 = 1k

k = 15.50

A large pizza with 4 toppings costs $20.

Using y = kx

20 = 4k

k = 20/4

k = 5

Here, the price does not vary directly with the number of toppings because the constant of proportionality is different.

b) A marathoner ran 5 miles in 40 minutes and 15 miles in 120 minutes.

Using y = kx

where,

y = 40

x = 5

y = kx

40 = 5k

k = 40/5

k = 8

Using y = kx

where,

y = 120

x = 15

y = kx

120 = 15k

k = 120/15

k = 8

The number of minutes vary directly with the number of miles. This is because the constant of proportionality is thesame in both cases.

Therefore, the second one(B) represents a direct variation and the first one (A) doesn't.

If the gradient of AB is 0, the coordinates of point A and B are (-4, 2) and (6, 2) respectively.

If the gradient of line AB is 0, it means that the line is horizontal. In this case, we can determine the coordinates of points A and B using the information given.

Since the midpoint of line AB is (1,2), we can infer that the average of the x-coordinates of A and B is 1, and the average of the y-coordinates is 2.

Let's assume that point A has coordinates (x₁, y₁) and point B has coordinates (x₂, y₂).

Since the midpoint of line AB is (1,2), we can write the following equations:

(x₁ + x₂) / 2 = 1 (1)

(y₁ + y₂) / 2 = 2 (2)

We also know that the length of line AB is 10 units.

Using the distance formula, we can express this as:

√((x₂ - x₁)² + (y₂ - y₁)²) = 10 (3)

Since the gradient of line AB is 0, the y-coordinates of points A and B must be the same. Therefore, y₁ = y₂. We can substitute this into equations (1) and (2):

(x₁ + x₂) / 2 = 1 (1')

y₁ = y₂ = 2 (2')

Now, let's substitute y₁ = y₂ = 2 into equation (3):

√((x₂ - x₁)² + (2 - 2)²) = 10

√((x₂ - x₁)²) = 10

(x₂ - x₁)² = 100

Taking the square root of both sides, we get:

x₂ - x₁ = ±10

Now, we have two cases to consider:

Case 1: x₂ - x₁ = 10

From equation (1'), we have:

(x₁ + x₁ + 10) / 2 = 1

2x₁ + 10 = 2

2x₁ = -8

x₁ = -4.

Substituting x₁ = -4 into equation (1), we find:

(-4 + x₂) / 2 = 1

-4 + x₂ = 2

x₂ = 6

Therefore, in this case, point A has coordinates (-4, 2), and point B has coordinates (6, 2).

Case 2: x₂ - x₁ = -10

From equation (1'), we have:

(x₁ + x₁ - 10) / 2 = 1

2x₁ - 10 = 2

2x₁ = 12

x₁ = 6

Substituting x₁ = 6 into equation (1), we find:

(6 + x₂) / 2 = 1

6 + x₂ = 2

x₂ = -4

Therefore, in this case, point A has coordinates (6, 2), and point B has coordinates (-4, 2).

To summarize, if the gradient of AB is 0, there are two possible solutions:

A(-4, 2) and B(6, 2)

A(6, 2) and B(-4, 2).

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The value that a number produces when it is multiplied by itself is known as the square root of the number. The square root is denoted by the radical sign. For instance, 16 Equals 4. The root symbol or surds is another name for the radical symbol.

The result of multiplying a number by itself yields its square value, while the square root of a number can be found by looking for a number that, when squared, yields the original value. It follows that a a = b if "a" is the square root of "b."

The square root of 50 is 7.07106781187.

The square root of 147 is 12.124355653

The square root of 96 is 9.79795897113

The square root of -8 is 2.82842712475i

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Answer: IT IS 1/12

Step-by-step explanation:

Because Felica is one of the girls that play and there is 7 boys and 4 others girls, its like saying we need to add 7 + 4 + 1 which is 12 the answer.

If i get this wrong, my apologies are to you, but I'm pretty sure my equation was correct

Thank me later

The the antioxidation activity of the substance has been found to depend on concentration in the activity of the substance has been found to depend on concentration are

a. Let B(c) = A(c) - L and reformulate the given initial value problem in terms of this new dependent variable, B. The new dependent variable B is related to A by B(c) = A(c) - L. Rearrange this to isolate A in terms of B as A(c) = B(c) + L.

Substitute the expression for A in terms of B into the original equation to obtain: d/dcb[c + L - B(c)] = k[B(c)]Where we apply the chain rule to obtain the left-hand side: dA/dc = d/dcb[c + L - B(c)] = -dB/dc.

b. Solve the initial value problem for B(c) and then determine the quantity A(c).We now have a separable first-order differential equation:-1/B dB = k/dc With boundary condition B(0) = -L Substituting in we get the solution ln(|B(c)|) = -kc + ln(|B(0)|) = kc + ln(L)Signs are ignored here since we are taking the absolute value, and the constant of integration is chosen to match the given initial value.

This can be solved for B as:B(c) = L e^(-kc)Hence the quantity A(c) is given by: A(c) = B(c) + L = L(1 - e^(-kc))

c. Determine the concentration at which 95% of the limiting antioxidation activity is achieved. Letting A(c) = 0.95L and solving for c gives: c = -ln(0.05)/k Therefore, the concentration at which 95% of the limiting antioxidation activity is achieved is -ln(0.05)/k.

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The distance Mrs. Smith covers is 3520 yards during the duration of the week by Friday morning.

One week has seven days in total.

Mrs. Smith walks half a mile each day after work, she walks a total of

0.5 miles/ day × 7 days/ week = 3.5 miles/ week

Now, if we calculate the distance on Friday morning, she must have walked four times till Friday morning since she has to walk after her work.

Therefore,

0.5 miles/ day × 4 days = 2 miles

To convert miles to yards, we can use the fact that there are 1760 yards in one mile:

2 miles/week × 1760 yards/mile = 3520 yards/week

Therefore, by Friday morning, Mrs. Smith will have walked 3520 yards.

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Answer:

y = x

Step-by-step explanation:

(0,0) and (15, 15)

Slope:

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

m=(15-0)/(15-0)

m=15/15

m = 1

Pt-Slope intercept:

y - y1 = m(x - x1)

y - 0 = 1(x - 0)

y - 0 = x

y = x

The equation x - 3 = 2 when evaluated is x = 5

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

x - 3 equal to 2.

Express the equation properly

So, we have the following representation

x - 3 = 2

Add 3 to both sides of the equation

This gives

x - 3 + 3 = 2 + 3

Evaluate the like terms

x = 5

Hence, the solution is x = 5

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Complete question

What is x - 3 equal to 2.

Evaluate

Answer:

Is there supposed to be a picture or no?

Step-by-step explanation:

Answer:  24c + 13

Step-by-step explanation:

f(x) = 6x + 1

(4c + 2)

f(4c + 2) = 6(4c + 2) + 1

f(4c + 2) = 24c + 13

Answer: f (4c + 2) = 24c + 13

Step-by-step explanation:

Given function

f(x) = 6x + 1

Function value that is asked to find

f (4c + 2)

Substitute values into the function

f (4c + 2) = 6 (4c + 2) + 1

Expand parentheses and apply the distributive property

f (4c + 2) = 6 · 4c + 6 · 2 + 1

f (4c + 2) = 24c + 12 + 1

Combine like terms

f (4c + 2) = 24c + (12 + 1)

f (4c + 2) = \(\boxed{24c+13}\)

Hope this helps!! :)

Please let me know if you have any questions

There are 24 sticks in pattern 6. The diagram indicates that one pattern is made up of one box built from four sticks.

A geometric pattern is a pattern made out of geometric forms that are generally repeated, much like a wallpaper design.

The given figure shows that one pattern consists of one box formed from the 4 sticks.

Pattrern 1 = 1 box  

Pattern 2 = 2 box

Pattern 6 = 6 box

1 box = 4 stick

Pattern 6 = 6 box = 6 ×4 = 24 sticks

Hence,there are 24 sticks in pattern 6.

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Answer:

Value of x = 5

Step-by-step explanation:

Given:

x + 4 = 3(x - 2)

Find:

Value of x

Computation:

x + 4 = 3(x - 2)

⇒ x + 4 = 3x - 6

⇒ x = 3x -6 - 4

⇒ x - 3x = -10

⇒-2x = - 10

⇒ x = -10 / - 2

Value of x = 5

Answer:

1. La ecuación vectorial de la línea es \(\begin{bmatrix} & x & \\ & y & \end{bmatrix} =\begin{bmatrix} & 4 & \\ & -2 & \end{bmatrix} + t \times \begin{bmatrix} & 2 & \\ & 5 & \end{bmatrix}\)

2. La ecuación de la recta es, y = -5·x - 6

Step-by-step explanation:

 1. El punto dado en la línea es A (4, -2), el vector paralelo a la línea es (2, 5)

Por tanto, la ecuación vectorial de la línea es;

\(\begin{bmatrix} & x & \\ & y & \end{bmatrix} =\begin{bmatrix} & 4 & \\ & -2 & \end{bmatrix} + t \times \begin{bmatrix} & 2 & \\ & 5 & \end{bmatrix}\)

Donde;

t = Cualquier número

2. El punto por el que pasa la recta es P (-2; 4)

La pendiente de la recta, m = -5

Por lo tanto, la ecuación de la línea en forma de punto y pendiente se presenta de la siguiente manera;

y - 4 = (-5) · (x - (-2)) = -5 · x - 10

∴ y - 4 = -5 · x - 10 + 4 = -5 · x - 6

La ecuación de la recta es, y = -5·x - 6

The dots are moving in a downward direction from left to right, so it is a negative trend.

Answer:

B. 15

Step-by-step explanation:

Step by Step Solution

More Icon

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "11.3" was replaced by "(113/10)".

Rearrange:

Rearrange the equation by subtracting what is to the right of the greater than sign from both sides of the inequality :

                    b-((113/10))>0  

Step by step solution :

STEP

1

:

           113

Simplify   ———

           10  

Equation at the end of step

1

:

      113

 b -  ———  > 0  

      10  

STEP

2

:

Rewriting the whole as an Equivalent Fraction

2.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  10  as the denominator :

         b     b • 10

    b =  —  =  ——————

         1       10  

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

2.2       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

b • 10 - (113)     10b - 113

——————————————  =  —————————

      10              10    

Equation at the end of step

2

:

 10b - 113

 —————————  > 0  

    10    

STEP

3

:

3.1    Multiply both sides by  10  

3.2    Divide both sides by  10  

     b-(113/10)  > 0

Solve Basic Inequality :

3.3      Add  113/10  to both sides

            b > 113/10

Inequality Plot :

3.4      Inequality plot for

        b  - 11.300  >  0

One solution was found :

b > 113/10

Which number is a solution of the inequality?

b > 11.3

The answers are 15,9,-14, and 4

15

Answer:

its C

i just took the test

AM = CN serves as additional proof that the triangles AMD and CNB are comparable according to the HL theorem.

A triangle is said to be right-angled if one of its angles is exactly 90 degrees. The total of the other two angles is 90 degrees. Perpendicular and the triangle's base are the sides that make up the right angle. The longest of the three sides, the third side is known as the hypotenuse.

Given Two right-angle triangles whose hypotenuse is equal.

From the HL-Theorem:

According to the hypotenuse-leg (HL) theorem, a right triangle is congruent if each of its hypotenuses and legs is congruent with its corresponding hypotenuse and legs in another right triangle. The HL theorem proves that these triangles are congruent.

This will work with any two right triangles that have the hypotenuse and one of the legs in proportion, as our selections of right triangles and their legs were arbitrary. Thus, the HL Similarity Theorem has been demonstrated.

Therefore, The additional information to prove if Both triangle AMD and CNB are similar by the HL theorem is AM = CN.

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Answer:

dont have question

Step-by-step explanation:

Answer:

161.557- so the second one

Step-by-step explanation:

A vector parallel to the curve described by the vector-valued function (t) when t = -4 is (-7, -11, -268). The t-values where l and e' are orthogonal are t = 1/2, t = 3/4, and t = -6/7.

The vector-valued function (t) = (1 + 2t, 3 - 4t, 67t) describes the curve C. To find a vector parallel to the curve when t = -4, we substitute t = -4 into the function and calculate the resulting vector. Plugging in t = -4, we get (-7, -11, -268), which represents a vector parallel to the curve at that particular point.

Next, we need to find the t-values where l and e' (two vectors) are orthogonal. Two vectors are orthogonal when their dot product is zero. Given the values t = 1/2, t = 3/4, and t = -6/7, we substitute these values into the vectors l and e' and calculate their dot product. If the dot product equals zero, it indicates orthogonality. Therefore, t = 1/2, t = 3/4, and t = -6/7 are the t-values where l and e' are orthogonal.

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The correct option is (B) the isometric transformation was possible due to the vertices' uniform 2 units to the right and 2 units downward displacement.

The process of turning a graph into a new graph using rotation, reflection, translation, and dilation is known as transformation.

An object is said to be rotated when it is turned by a specific amount in either the clockwise or counterclockwise directions on an x-y plane.

Reflection turns an object into a mirror image that is identical in terms of size and shape with just the coordinates altered.

Moving an item up, down, left, or right on a coordinate axis is known as translation.

Dilation is the process of modifying an object's size; the original object is either compressed or enlarged by a specific scale factor.

So, the coordinates for the object ABC in the image are A (-2, 5), B (-5, 3), C(1, 3), and.

The picture's coordinates are A'(0,3), B'(-5,-3), and C' (3, -5).

The coordinates have undergone a translational transformation.

The vertices all shifted 2 units to the right and 2 units down, allowing an isometric transformation to be applied.

Therefore, the correct option is (B) the isometric transformation was possible due to the vertices' uniform 2 units to the right and 2 units downward displacement.

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Complete question:

Which describes the transformation that could have been applied to triangle ABC?

a. A dilation could have been applied because all of the vertices decreased by 2 units.

b. An isometric transformation could have been applied because all of the vertices moved 2 units right and 2 units down.

c. A dilation could have been applied because all of the vertices increased 2 units.

d. An isometric transformation could have been applied because all of the vertices moved 2 units left and 2 units up.

The circumference of a circle with a radius of 3 ft is greater than the distance around a semicircle with a diameter of 16 ft by approximately 2.84 ft.

The circumference of a circle is calculated using the formula C = 2πr, where r is the radius. For the given circle with a radius of 3 ft, the circumference would be C = 2π(3) = 6π ft.

The distance around a semicircle is calculated by finding half the circumference of the corresponding full circle. In this case, the diameter of the semicircle is 16 ft, which means the corresponding full circle has a radius of 8 ft. The circumference of the full circle is C = 2π(8) = 16π ft. Therefore, the distance around the semicircle is half of that, which is 8π ft.

Comparing the two values, 6π ft is greater than 8π ft by approximately 2.84 ft. Hence, the circumference of the circle with radius 3 ft is greater than the distance around the semicircle with a diameter of 16 ft by approximately 2.84 ft.


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Answer:

so the Domain:

{5, -5, 6,−6}

Range:  {1,4,2,8,3}

functon no

Since x=−5 produces y=4 and y=3, the relation (5,1),(−5,4),(6,2),(−6,8),(−5,3)is not function.

Step-by-step explanation:

domain is normally x and range in most the time y, this is what i was taught and i hope it helps and is right

Answer:

1.5 sweaters or 1 and half of a sweater

Step-by-step explanation:

you would multiply 6 by 3/12 and get 1 and a half

the diagonals of this parallelogram intersect (3, 1.5)

A unique kind of quadrilateral known as a parallelogram is defined by having both pairs of opposite sides parallel and equal. An ABCD parallelogram with AB II CD and AD II BC is seen in the provided illustration. As well, as AB = CD and AD = BC.

Similar to how the area of a rectangle is calculated, the formula for calculating the area of a parallelogram is base times height.

The diagonals intersect at point o.

so, x is the midpoint.

In parallelogram diagonals bisects each other.

Now, consider the points: A (0,0)  B (4,0) C (6,3) D (2,3)

So, A (0,0) and C (6,3)

The midpoint (x₀,y₀) = [(x₁+x₂)/2, (y₁+y₂)/2]

thus, x₀ = (0+6)/2 = 6/2 = 3

y₀ = (0+3) /2 = 3/2 = 1.5

Thus, the diagonals of this parallelogram intersect: (3, 1.5)

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Answer:

Explanation:

a) To get the time taken to reach the ground, we set the horizontal and vertical positions equal to one another

Mathematically, we have that as:

We can proceed to solve for t by using the quadratic equation

We have that as:

a is the coefficient of t^2 which is 4 , b is the coefficient of t which is 2, c is the last number which is -25

Substituting the values, we have it that:

Since t cannot be negative, we have the time as 2.26 seconds

b) To get her distance from the cliff, we find the value of z(t)

We simply substitute t into the equation for z(t)

We have that as:

The given curves are `y = x + 1, y = 0, x = 0 and x = 4` and we are supposed to find the volume `V` of the solid obtained by rotating the region bounded by the given curves about the x-axis.

The region is shown below:Region bounded by y = x + 1, y = 0, x = 0 and x = 4We can observe that the region is a right-angled triangle with perpendicular `4` and base `1`. Now, we need to rotate this right-angled triangle about the x-axis to form a solid of revolution. The solid of revolution obtained is shown below:Solid of revolution obtained by rotating the region about the x-axis Since the region is rotated about the x-axis, the axis of rotation is `x-axis`.

So, the formula for volume of the solid of revolution is given by:`V = pi * ∫[a, b] y^2 dx`Here, the limits of integration are `a = 0` and `b = 4`.We need to express `y` in terms of `x`.Since, `y = x + 1`, we get`x = y - 1`Substituting this value of `x` in `x = 4`, we get`y - 1 = 4``y = 5`So, the limits of integration for `y` are `0 to 5`.So, we have to evaluate the integral:`V = pi * ∫[0, 5] (y - 1)^2 dx`

Simplifying this, we get:`V = pi * ∫[0, 5] (y^2 - 2y + 1) dy``V = pi * (∫[0, 5] y^2 dy - 2∫[0, 5] y dy + ∫[0, 5] dy)``V = pi * [y^3/3 - y^2 + y] [0, 5]``V = pi * [(5^3/3 - 5^2 + 5) - (0)]``V = pi * [(125/3 - 25 + 5)]``V = pi * [100/3]`

Therefore, the volume `V` of the solid obtained by rotating the region bounded by the given curves about the x-axis is `V = (100/3) pi` (in cubic units).

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Answer:

relation

Step-by-step explanation:

The number of bacteria that represents y at the end of x days will be \(y=(500)(2)^{x}\)

As per the given data on the day 0, there are 500 bacteria in a dish.

The number of bacteria that doubles every day after that.

Here we have to determine that how many bacteria which represent y are there after x number of days.

Therefore, the number of bacteria after every day will form a geometric progression (G.P) with the first term as a = 500 and the common ratio as r = 2

Therefore \(\mathrm{a}_3=\mathrm{ar}^2=(500)(2)^2=2000\)

Therefore, the number of bacteria at the end of 2nd day will be 480

\($a_5=a^4=(500)(2)^4=8000\)

And \($\mathrm{a}_{\mathrm{n}+1}=\mathrm{ar}^{\mathrm{n}}\)

\($\mathrm{a}_{\mathrm{n}+1}\) represents y and n represents x

\(y=(500)(2)^{\mathrm{x}}\)

Thus the number of bacteria at the end of x days will be \((500)(2)^{x}$=y\)

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The interquartile range (IQR) is a measure of the spread or variability of the middle 50 percent of the data.

The interquartile range (IQR) is a statistical measure that describes the spread or dispersion of the middle 50 percent of the data. It is calculated as the difference between the third quartile (Q3) and the first quartile (Q1) of a dataset.

The quartiles divide a dataset into four equal parts, each representing 25 percent of the data. The first quartile (Q1) represents the lower boundary of the middle 50 percent, while the third quartile (Q3) represents the upper boundary of the middle 50 percent. The IQR captures the range of values within this middle range.

By focusing on the middle 50 percent of the data and excluding the extreme values, the interquartile range provides a measure of variability that is less affected by outliers or extreme values. It is commonly used in descriptive statistics and data analysis to understand the spread and distribution of a dataset, particularly when the data is not symmetrically distributed or contains outliers.

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the value of side z is 52.5

What is an isosceles triangle ??

An isosceles triangle in geometry is one with at least two sides that are of equal length. Both having exactly two sides of equal length and having at least two sides of equal length are acceptable specifications, with the latter version containing the equilateral triangle as an exception. The faces of bipyramids, the golden triangle, the isosceles right triangle, and some Catalan solids are all examples of isosceles triangles.

in this figure, it is an isosceles triangle as two sides of the triangle are equal.

In the given ΔABC,

given ΔDFE ≅ ΔCFB

x= 45*2.5 = 112.5

z = 112.5-60= 52.5

Hence the value of side z is 52.5

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