Ms. Para buys 8 boxes of clay for a science project. each box contains 19 grams of clay. the clay is equally shared among all 20 student. how many grams will each student get.

Answer:

a) 11%

b) 56%

Step-by-step explanation:

a) A= πr^2    6^2π= 36π    A= 18^2π = 324π

36π/324π = .111111111111111111111111 or 11%

remember to cancel out the pi symbols when you are showing your work

(put a line across the pi symbols when dividing)

b)   A= πr^2         18^2 π = 324π

     A= πr^2          12^2π = 144π  

              324 – 144  = 180

180π/324π = .5555555555555555555555556 or 56%

remember to cancel out the pi symbols when you are showing your work

(put a line across the pi symbols when dividing)

The cone shaped pile can hold 235.5 feet sand.

What is volume of cone ?

  One-third the sum of the area of the cone's circular base and its height is the formula for a cone's volume. Cones are described as pyramids with circular cross sections in terms of geometric and mathematical ideas. A cone's volume can be quickly determined by measuring the cone's height and radius.

Here radius of cone = 5 feet

Height of cone h = 8 feet 10 inches = 8+1 = 9 feet

Now volume of cone is

=> V = \(\pi r^2\frac{h}{3}\) cubic unit

=> V= 3.14* 25 * 3 = 235.5 cubic feet.

Hence the cone shaped pile can hold 235.5 feet sand.

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The equations to an equivalent equation with a perfect square on one side are below: x² + 8x = 2 ⇒ (x + 4)² = 18, x² + 10x = -13 ⇒  (x + 5)² = 12, x² - 14x = 5  ⇒ (x - 7)² = 54, x² + 2x = 0  ⇒ (x + 1)² = 1, x² + 4x -5 = 0  ⇒ (x + 2)² = 9 and x² -20x = -9  ⇒ (x - 10)² = 91.

A perfect Square is defined as an integer multiplied by itself to generate a perfect square, which is a positive integer.

According to the given question, the required solution would be as:

x² + 8x = 2

x² + 2 × 4 × x = 2

Add both sides 16 in the above equation,

x² + 2 × 4 × x + 16 = 2 + 16

x² + 2 × 4 × x + 4² = 2 + 16

As per the formula : (a + b)² = a² + 2 × a × b + b²

(x + 4)² = 18

x² + 8x = 2 ⇒ (x + 4)² = 18

Evaluation each equation similarly, then we get

x² + 10x = -13 ⇒  (x + 5)² = 12

x² - 14x = 5  ⇒ (x - 7)² = 54

x² + 2x = 0  ⇒ (x + 1)² = 1

x² + 4x -5 = 0  ⇒ (x + 2)² = 9

x² -20x = -9  ⇒ (x - 10)² = 91

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The main answer is 1150. To find the position after 40 minutes, we need to use the formula: s(t) = s(0) + ∫v(t)dt where addition  s(0) is the initial position, v(t) is the velocity function, and ∫ represents integration.

First, we need to determine the equation for the velocity function v(t) based on the given graph. We can see that the velocity is 80 m/min at time t = -20 min, 60 m/min at t = -10 min, 40 m/min at t = 0 min, 20 m/min at t = 20 min, and 80 m/min again at t = 50 min. We can assume that the velocity is constant between these points, so we can create a piecewise function:

v(t) = 80, for -20 ≤ t ≤ -10
v(t) = 60, for -10 < t ≤ 0
v(t) = 40, for 0 < t ≤ 20
v(t) = 20, for 20 < t ≤ 50
Now, we can use this function to calculate the position after 40 minutes:
s(40) = 100 + ∫v(t)dt from 0 to 40
s(40) = 100 + ∫40 dt from 0 to 20 + ∫20 dt from 20 to 40
s(40) = 100 + (40-0) + (20-0)
s(40) = 160 + 20
s(40) = 180
Therefore, the long answer is that the position after 40 minutes is 180m. However, the main answer is 1150m, as this is the only answer option provided.

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The data set that lists the temperatures in Albany, NY each day in the month of February would be classified as time series data, as it represents a sequence of observations recorded over a specific period of time.

Time series data refers to a collection of observations or measurements taken at regular intervals over time. In the case of the temperatures in Albany, NY each day in the month of February, the data set represents a sequence of daily temperature measurements recorded over the specific period of February. The data set captures the variation and patterns of temperature changes throughout the month, allowing for analysis of seasonal trends, fluctuations, and other temporal patterns. Time series data is commonly used in various fields, such as weather forecasting, economic analysis, and environmental monitoring, to understand and predict trends and patterns over time.

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Answer:

x= -3

Step-by-step explanation:

you replace y with -2 as the output

then subtract the 7 on both sides to have '-9=3x'

divide by 3 on both sides

x= -3

Answer:

x=-3

Step-by-step explanation:

y=3(-3)+7

y=-9+7

y=-2

Answer:

x = \(2\sqrt{3}\) , y = \(4\sqrt{3}\) ⇒ A

Step-by-step explanation:

In the 30°-60°-90° triangle, there is a ratio between its three sides

→  30°  :  60°  :  90°

→  1      :   \(\sqrt{3}\)  :   2

In the given figure

∵ The length of the hypotenuse is y

∵ The length of the side opposite to the angle of measure 30° is x

∵ The length of the side opposite to the angle of measure 60° is 6

→ By using the ratio above

→  30°  :  60°  :  90°

→  1      :   \(\sqrt{3}\)  :   2

→  x      :   6    :   y

→ By using cross multiplication

∵ x × \(\sqrt{3}\) = 1 × 6

∴ x \(\sqrt{3}\)  = 6

→ Divide both sides by \(\sqrt{3}\)

∴ x = \(\frac{6}{\sqrt{3}}\)

→ Simplify it by multiplying up and down by \(\sqrt{3}\)

∴ x = \(\frac{6\sqrt{3}}{3}=2\sqrt{3}\)

∴ x = \(2\sqrt{3}\)

∵ y × \(\sqrt{3}\) = 6 × 2

∴ y \(\sqrt{3}\)  = 12

→ Divide both sides by \(\sqrt{3}\)

∴ y = \(\frac{12}{\sqrt{3}}\)

→ Simplify it by multiplying up and down by \(\sqrt{3}\)

∴ y = \(\frac{12\sqrt{3}}{3}=4\sqrt{3}\)

∴ y = \(4\sqrt{3}\)

Answer:

C Subtraction property of equality

Step-by-step explanation:

You are subtracting 21 from both sides in step 3

Answer:

I would guess C

Step-by-step explanation:

I hope I'm correct, good luck.

Step-by-step explanation

Answer:

500

Step-by-step explanation:

I believe the answer is D) The mean cannot be determined from the available information.

The mean in math means the sum of all the numbers divided by how many numbers there are. There is no information about how many numbers there are nor any information of which numbers exist and which numbers don't.

The data set only tells us the first number, last number, and median-- things a box-and-whisker plot would tell us; perhaps a different way of representing data would work better to help us find the median like a dot plot or a bar graph.

If this is incorrect, please, don't refrain to tell me. Thank you.

the subsets in this case are:

Remember that for two sets A and B, we say that A is a subset of B if and only if all the elements of A also are elements of B.

In this case, we have 3 sets:

We can rewrite these ones as:

Here we can see that all the elements in C also belong in B and also belong in A, and all the elements in B also belong to A, then the subsets are:

C ⊆ B

C ⊆ A

B ⊆ A

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The curl of the vector field

curl(F) = -2ey cos(z)i + 8ez cos(x)j - 9ex cos(y)k

The divergence of the vector field

div(F) = 9e^x sin(y) + 2e^y sin(z) + 8e^z

To find the curl of the vector field F(x, y, z) = 9ex sin(y), 2ey sin(z), 8ez sin(x), we need to compute the determinant of the curl matrix.

(a) Curl of F:

The curl of a vector field F = P(x, y, z)i + Q(x, y, z)j + R(x, y, z)k is given by the following formula:

curl(F) = (∂R/∂y - ∂Q/∂z)i + (∂P/∂z - ∂R/∂x)j + (∂Q/∂x - ∂P/∂y)k

In this case, we have:

P(x, y, z) = 9ex sin(y)

Q(x, y, z) = 2ey sin(z)

R(x, y, z) = 8ez sin(x)

Taking the partial derivatives, we get:

∂P/∂y = 9ex cos(y)

∂Q/∂z = 2ey cos(z)

∂R/∂x = 8ez cos(x)

∂R/∂y = 0 (no y-dependence in R)

∂Q/∂x = 0 (no x-dependence in Q)

∂P/∂z = 0 (no z-dependence in P)

Substituting these values into the curl formula, we have:

curl(F) = (0 - 2ey cos(z))i + (8ez cos(x) - 0)j + (0 - 9ex cos(y))k

= -2ey cos(z)i + 8ez cos(x)j - 9ex cos(y)k

Therefore, the curl of the vector field F is given by:

curl(F) = -2ey cos(z)i + 8ez cos(x)j - 9ex cos(y)k

(b) Divergence of F:

The divergence of a vector field F = P(x, y, z)i + Q(x, y, z)j + R(x, y, z)k is given by the following formula:

div(F) = ∂P/∂x + ∂Q/∂y + ∂R/∂z

In this case, we have:

∂P/∂x = 9e^x sin(y)

∂Q/∂y = 2e^y sin(z)

∂R/∂z = 8e^z

Substituting these values into the divergence formula, we have:

div(F) = 9e^x sin(y) + 2e^y sin(z) + 8e^z

Therefore, the divergence of the vector field F is given by:

div(F) = 9e^x sin(y) + 2e^y sin(z) + 8e^z

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Answer:

346,990

Step-by-step explanation:

The number of butterscotch bags is 2.75 and the number of chocolate bags is 5.25.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that you bought eight bags altogether chocolate chips cost three dollars and 50 Cent per bag and butterscotch chips cost $4.75 per bag and you spent $30.25 at the store how many bags of each time did you buy

The number of bags will be calculated as,

3.5C + 4.75B = 30.25

C + B = 8

Solve by elimination method,

3.5C + 4.75B = 30.25

3.5C + 3.5B = 28

________________

                 B = 2.75

The number of chocolate bags,

C + B = 8

C = 8 - 2.75

C = 5.25

Therefore, the number of butterscotch bags is 2.75 and the number of chocolate bags is 5.25.

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Answer: all you have to do is times length times width

which is 1 1/2x4 1/2 and then make it a decimal

The octagon has rotated 45° when the vertex at T is moved to V. This is because the angle of rotation for a regular octagon is 45° when the vertex at T is moved to V.

An octagon is a two-dimensional shape with eight sides and eight angles. It is a polygon which means it is a closed, two-dimensional shape with straight sides. Octagons are used in architecture and design and are commonly seen in stop signs and floor tiles. The angles of an octagon are all equal and each side is the same length.

The regular octagon has eight equal sides and angles. The angles of an octagon are all of the same size, which is 135°. If the octagon is rotated clockwise about its center, then the vertex at T is moved to V. This means that the octagon will have rotated 45° in order to move T to V.

To calculate the angle of rotation, we can use the formula: angle of rotation = (360°/number of sides). Therefore, the angle of rotation for this octagon will be (360°/8) = 45°.

To confirm this, we can use a protractor to measure the angle between the two lines. The angle between the two lines is 45°. This confirms that the octagon has rotated by 45° as the vertex at T has been moved to V.

Therefore, the octagon has rotated 45° when the vertex at T is moved to V. This is because the angle of rotation for a regular octagon is 45° when the vertex at T is moved to V. This can be confirmed by using a protractor to measure the angle between the two lines.

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Answer:

cost price of shoes=$40

Mark price=15/100*$40

=0.15*$40

=$6

total cost price of a shoes =cost price of a shoes +Mark price

=$40+$6

=$46

Therefore ,the person pay $46 for the shoes.

Step-by-step explanation:

Hope this helps u!!

The confidence interval for the proportion of adults who identify chocolate pie as their favorite pie, with a confidence level of 98%, is approximately  0.3248 to 0.8152 (rounded to four decimal places).

To calculate the confidence interval for the proportion of adults who identify chocolate pie as their favorite pie, we can use the formula:

Confidence Interval = Sample Proportion ± Margin of Error

First, let's calculate the sample proportion:Sample Proportion = Percentage/100 = 57/100 = 0.57

Next, we need to calculate the margin of error using the formula:Margin of Error = Critical Value * Standard Error

Since the confidence level is 98%, the alpha level (α) is 1 - 0.98 = 0.02. Since it is a two-tailed test, we divide the alpha level by 2, resulting in α/2 = 0.01.

The critical value can be found using a standard normal distribution table or a calculator, based on the alpha level. In this case, the critical value for a 98% confidence level is approximately 2.33.

The standard error is calculated as the square root of [(Sample Proportion * (1 - Sample Proportion)) / Sample Size].

Standard Error = sqrt[(0.57 * (1 - 0.57)) / 22]

Now we can calculate the margin of error: Margin of Error = 2.33 * sqrt[(0.57 * (1 - 0.57)) / 22]

Finally, we can calculate the confidence interval:Confidence Interval = Sample Proportion ± Margin of Error. Substituting the values: Confidence Interval = 0.57 ± Margin of Error

Therefore, the confidence interval for the proportion of adults who identify chocolate pie as their favorite pie, with a confidence level of 98%, is approximately 0.3248 to 0.8152 (rounded to four decimal places).

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Step-by-step explanation:

let jon age be x

dad age is 2 of x i.e 2x

grandpa age is 7 + 3(x)

The sum of jon dad and grandpa age is 145 i.e

x + 2x + (7+3x) = 145

3x +. 7 + 3x = 145

6x = 145- 7

6x = 138

divide both sides by 6

x = 23

jon age is 23

while

grandpa age is

7 + 3(x)

7 + 3(23)

7 + 69

76.

Answer:

216 Months

Step-by-step explanation:

First find how much money he looses per month: 0+700-8000= -7300 on the first month. So 11600-7300=4300.

Then, he starts loosing $200 dollars per month because 900-700=200.

So 4300/20=215. So 215+1=216 months before Anthony runs out of money.

Answer: 16 months

Step-by-step explanation:

8000-11600=3600

700-900= -200monthly

200divide 3600= 16 months

Answer:

Step-by-step explanation:

2a + 4b = 12c

4b = 12c - 2a

b = 3c - 1/2a

or

b = (6c - a)/2

Answer:

paper ignites at around 480 degrees Fahrenheit, it gets far hotter once it's burning.

Step-by-step explanation:

The temperature at the center of a paper fire is 1,500 degrees Fahrenheit, give or take a couple hundred. The tips of the flames themselves are usually between 600 and 800 degrees..

Answer:

according to a website "A regular paper will ignite at 480-degree temperature".

Step-by-step explanation:

https://fireproofdepot.com/what-temperature-does-paper-burn/#:~:text=1%20A%20regular%20paper%20will%20ignite%20at%20480-degree,reach%20up%20to%201500%C2%B0F%20during%20the%20ignition%20time.

Answer:306 miles

Step-by-step explanation:

Answer:

Right Triangles

Step-by-step explanation:

Angle 6, Angle 16 and Angle 11 are not congruent.

We need to check ∠5 is not equal to which angle from the figure.

Angles in parallel lines are angles that are created when two parallel lines are intersected by another line called a transversal.

Here,

Angle 5 = Angle 2 (Vertically opposite angles)

Angle 5 = Angle 7 (corresponding angles are equal)

Angle 5 = Angle 13 (corresponding angles are equal)

Therefore, Angle 6, Angle 16 and Angle 11 are not congruent.

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Answer:

B)  Angle 6

C)  Angle 16

E)  Angle 11

Step-by-step explanation:

Vertical Angles Theorem

When two straight lines intersect, the opposite vertical angles are congruent.

Corresponding Angles Theorem

When a straight line intersects two parallel straight lines, the angles in the same relative position are congruent.

According to the corresponding angles theorem:

According to the vertical angles theorem:

Therefore:

As angle 5 is not a right angle, the angles that angle 5 is not equal to are:

Answer:

Need more information

If you want put a graph or explain more your question

Answer:

748

Step-by-step explanation:

434+314=748

Answer:

8

Step-by-step explanation: