Naomi made sand art bottles to sell at her school's craft fair. First, she bought 4 kilograms of sand in different colors. Then, she filled as many 100-gram bottles as she could. How many sand art bottles did Naomi make?

Answer:

can you please send the diagram for it to be clear

The answer to the expression 2b x b is simply 2b^2. Exponentiation is a mathematical operation that raises a number to a power, and in this case, b is raised to the power of 2.

Alternatively, if exponentiation is not allowed, the answer to the expression is simply 2b * b, which can be simplified to 2b^2 as well.

So, the answer to the expression 2b x b is 2b^2, regardless of whether or not exponentiation is used.

The expression 2b x b represents the product of two scalars, 2 and b, multiplied by a scalar b.

The expression could represent a variety of quantities in mathematics and science, including the area of a rectangle, the volume of a cube, or the kinetic energy of an object, among others.

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Answer: $150

Step-by-step explanation:

From the question, we are informed that the balance of Stephanies average balance checking account at the beginning of last cycle was $200 and that the only transaction for the cycle was a check that Stephanie wrote for $100 which cleared exactly halfway through the cycle.

Since the $100 check was cleared halfway, the amount that Stephanies checking account will pay interest last cycle will be for us to deduct half of $100 from $200. This will be:

= $200 - 1/2($100)

= $200 - $50

= $150

A 99% confidence interval for the proportion of college students who smoke for the given standard deviation is  (0.021. 0.045).

What is standard deviation?

Standard Deviation is a measure that shows what quantity variation (such as unfold, dispersion, spread,) from the mean exists. the quality deviation indicates a “typical” deviation from the mean. it's a well-liked live of variability as a result of it returns to the first units of live of the info set.

Main body:

formula for confidence interval is :

m = p-bar ± z*√p(1-p)/n

given information =

n= 650

p - bar = 25/650 = 1/26

C.I. = 99% = 0.99

we need to find value of 0.99 in z -table

z = 2.33

substituting value ,

0.038 ± 2.33√( 0.038(1-0.038))/650

0.038 ± 2.33 * 0.075

0.038 ± 0.017

(0.021. 0.045)

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Answer:

3(4 + n) = n + 18

n = 3

Step-by-step explanation:

because the sum of 4 and a number is multiplied by three. That equals the number plus 18. N = 3. in the image below are the steps you can take to solve the equation.

Answer:

Angle FDG is 42°

Step-by-step explanation:

the whole angle GDE is an obtuse angle (greater than 90° but less than 180°), but a line is drawn at the middle to split it into 2.Each will be an acute angle.This means our answer must be acute.Mathematically ,

x+86=128

X=128-86

X=42°

to be sure,when an obtuse angle is split into two angles,it becomes 2 acute angles.

The person's total salary over the first 6 years is $231,750.

To determine the person's total salary over the first 6 years, we need to calculate the sum of the salary for each year.

Given information:

- Initial salary: $34,000

- Annual raise: $1,850

- Number of years: 6

To calculate the total salary, we can use the arithmetic progression formula:

[ S = frac{n}{2} left(2a + (n - 1)dright) ]

Where:

- ( S ) is the sum of the salaries

- ( n ) is the number of terms (years)

- ( a ) is the first term (initial salary)

- ( d ) is the common difference (annual raise)

Substituting the given values, we have:

[ S = frac{6}{2} left(2(34000) + (6 - 1)(1850)right) ]

Simplifying the expression:

[ S = 3 left( 68000 + 5 times 1850 right) ]

[ S = 3 left( 68000 + 9250 right) ]

[ S = 3 times 77250 ]

[ S = 231750 ]

Therefore, the person's total salary over the first 6 years is $231,750.

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Answer:

\(q = 22\)

Step-by-step explanation:

The angle measure of a straight line is (180) degrees As given in the picture, line (AC) is a straight line, thus its angle measure is (180) degrees. Angles (ABD) and (DBC) make up line (AC). Therefore, one can conclude that the sum of angles (ABD) and (DBC) is (180) degrees. Form an equation, simplify and use inverse operations to solve for the unknown parameter (q).

\((<ABD) + (<DBC) = (AC)\)

Substitute for the angle measures,

\((7q-46)+(3q+6)=180\)

Simplify,

\(10q-40=180\)

Inverse operations,

\(10q-40=180\\\\10q = 220\\\\q = 22\)

Answer:

need pts

Step-by-step explanation:

The phrase "number of values for which a certain condition holds" is referred to as multiplicity. The phrase, for instance, can be used to describe the magnitude of the totient valence function or the frequency with which a given polynomial equation has a root at a specific location.

Let z_0 be a root of a function f, and let n be the least positive integer n such that f^((n))(z_0)!=0. Then the power series of f about z_0 begins with the nth term,

f(z)=sum_(j=n)^infty1/(j!)(partial^jf)/(partialz^j)|_(z=z_0)(z-z_0)^j,

and f is said to have a root of multiplicity (or "order") n. If n=1, the root is called a simple root '

The multiplicity of a member of a multiset in mathematics is the number of times the member appears in the multiset. The multiplicity of a root, for instance, is how many times a given polynomial has a root at a particular point.

It's crucial to understand the concept of multiplicity in order to correctly count without mentioning exceptions (for example, double roots counted twice). Thus, "counted with multiplicity" is used.

This can be highlighted by counting the number of different elements, as in "the number of separate roots," if multiplicity is disregarded. However, multiplicity is always taken into account when a set (as opposed to a multiset) is established, therefore the word "different" is not necessary.

Hence ,Multiplicity means the quality or state of being multiple or various. and

the number of components in a system (such as a multiplet or a group of energy levels)

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Let z_0 be a root of a function f, and let n be the least positive integer n such that f^((n))(z_0)!=0. Then the power series of f about z_0 begins with the nth term,

f(z)=sum_(j=n)^infty1/(j!)(partial^jf)/(partialz^j)|_(z=z_0)(z-z_0)^j,

and f is said to have a root of multiplicity (or "order") n. If n=1, the root is called a simple root '

The multiplicity of a member of a multiset in mathematics is the number of times the member appears in the multiset. The multiplicity of a root, for instance, is how many times a given polynomial has a root at a particular point.

Answer:

(a-b) {a raise2+b raise 2 - ab}

Step-by-step explanation:

Answer:

\((a-b)(a^2+ab+b^2)\)

Step-by-step explanation:

\(a^3-b^3=(a-b)(a^2+ab+b^2)\)

A right circular cylinder can be generated by rotating a rectangle of perimeter p about one of its sides. The dimensions of the rectangle that will generate the cylinder of max volume are l = p/6 and w = p/2 - l = 2p/3.

Explanation: Let l and w be the dimensions of the rectangle of perimeter p.

That is, the rectangle's perimeter is given by p = 2l + 2w or p/2 = l + w. Therefore, the width w = p/2 - l. The area of the rectangle is given by lw. When the rectangle is rotated around the side of length w, it generates a cylinder of height l and radius w.

The volume of the cylinder is given by V = πr²h = πw²l. Substituting w = p/2 - l, we obtain V = π(p/2 - l)²l = π(p/2)²l - 2π(p/2)l² + πl³.

The volume function can be obtained by differentiating V with respect to l, setting the derivative equal to 0, and solving for l. The derivative of V with respect to l is given by dV/dl = π(p/2)² - 4π(p/2)l + 3πl².

Setting dV/dl = 0 and solving for l, we obtain l = p/6.The dimensions of the rectangle that will generate the cylinder of max volume are l = p/6 and w = p/2 - l = 2p/3.

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Answer:

because AB//DE

so DÊC=BÂC ( 2 straight lines are parallel and have the same internal angle)

because ACD is the outer angle of the triangle ABC so ACD= ABC+BÂC

because DÊC=BÂC

so ACD= ABC+ DÊC

Given that mean= 6.56 and standard deviation(σ)= 1.19

a) P(X ≤ 5)= ( (X-µ)/ σ) < (5- 6.56)/ 1.19)

                = 0.094946

P(X ≤ 5)= 0.95

So 0.95 proportion of the survey would think $5 is too expensive for a sandwich.

b) P(X ≥ 6.75) = ( (X-µ)/ σ) < (6.75- 6.56)/ 1.19)

                      = 0.43656

0.43656 proportion of people surveyed would be willing to pay more than $6.75 for a sandwich.

c)  P(X ≤ x)= 0.35

                 = P((x- µ)/ σ ≤ (x- 6.65)/ 1.19)

                  0.35

x= (-0.3853) (1.19) + 6.56

 = 6.1015

6.1015  is the 35th percentile for how much people are willing to pay for a sandwich.

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Answer:

Y is less than or equal to 2/5x+1

Answer:

it is 100% b

Step-by-step explanation:

Answer:

£ 210  &  £ 270

Step-by-step explanation:

Amount =  £480

Ratio = 7 : 9

Total parts = 7+9 = 16

\(\dfrac{7}{16}*480=7 * 30\) =  £ 210

\(\dfrac{9}{16}*480=9*30= 270\)

Answer:

s/84π = 150°/360°

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Answer:

The answer is B

Step-by-step explanation:

Answer:

- 10k - 150

Step-by-step explanation:

Given

10(4k - 12) - 10(3 + 5k) ← distribute both parenthesis

= 40k - 120 - 30 - 50k ← collect like terms

= - 10k - 150

Answer:

All solutions or infinite.

Step-by-step explanation:

Turn 2y = -4x + 6 into standard form - divide by 2

Y = -2x + 3

2x + y = 3

Substitute the y equation in for y.

2x - 2x + 3 = 3

The x variables cancel out.

3 = 3

Which is true so it means all solutions.

Hope this helps.

The probability that the sum of the faces is 7 = 15/216

The value of m = 15 and the value of n = 216

In this question, we have been given three regular dice are rolled simultaneously.

We need to find the probability that the sum of the faces is 7.

When three dice are rolled simultaneously, the total number of outcomes

n(S) = 6 * 6 * 6

n(S) = 216

Let event A: sum of the faces is 7

A = {(1, 2, 4), (1, 4, 2), (4, 1, 2), (4, 2, 1), (2, 1, 4), (2, 4, 1), (1, 3, 3), (3, 3, 1), (3, 1, 3), (2, 2, 3), (2, 3, 2), (3, 2, 2), (1, 5, 1), (5, 1, 1), (1, 1, 5)}

n(A) = 15

So, the probability that the sum of the faces is 7 = 15/216

Hence, if the probability that the sum of the faces is 7 can be represented by m/n in simplest form then m = 15 and n = 216

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Answer:

Experimental units, factors & treatments in experiment.

Step-by-step explanation:

Experimental Units are the 60 restaurants.

Factors are the : Menu description & price

Treatments in experimental design : Healthy Low Price, Healthy Medium Price, Healthy High price & Value low price, Value medium price, Value high price.

Answer:

it is 1

Step-by-step explanation:

Answer:

38.6 units.

Step-by-step explanation:

The given figure is composed of a parallelogram and one  semicircle.

We need to find the perimeter of the parallelogram.

Perimeter = sum of all sides

ATQ,

P = 9+8+9+(2πr/2)

i.e.

\(P=26+\pi r\\\\=26+3.14\times 4\\\\=38.56\ \text{unit}\)

or

= 38.6 units

So, the perimeter of the figure is equal to 38.6 units.

Answer:

The volume of the aquarium can be found by multiplying its length, width, and height:

Volume = length x width x height

Volume = 19 in x 15 in x 12 in

Volume = 3,420 cubic inches

Therefore, when the aquarium is full, it can hold 3,420 cubic inches of water.

Step-by-step explanation:

the total distance traveled by the particle over the time period is 14/3 meters.

To find the displacement of the particle over the time period, we need to integrate the velocity function v(t) over the given interval.

A) Displacement:

The displacement is given by the definite integral of the velocity function v(t) over the interval [1, 6]:

Displacement = ∫[1, 6] (t^2 - 2t - 8) dt

To evaluate this integral, we can use the power rule of integration:

Displacement = [(1/3) * t^3 - t^2 - 8t] evaluated from 1 to 6

= [(1/3) * (6^3) - 6^2 - 8 * 6] - [(1/3) * (1^3) - 1^2 - 8 * 1]

= [72 - 36 - 48] - [1/3 - 1 - 8]

= -12 - (-22/3)

= -12 + 22/3

= (-36 + 22)/3

= -14/3

Therefore, the displacement of the particle over the time period is -14/3 meters.

B) Total Distance:

To find the total distance traveled by the particle over the time period, we need to consider the absolute value of the velocity function and integrate it over the interval [1, 6]:

Total Distance = ∫[1, 6] |t^2 - 2t - 8| dt

Since the velocity function is already non-negative for the given interval, we can calculate the total distance by evaluating the integral of v(t) directly:

Total Distance = ∫[1, 6] (t^2 - 2t - 8) dt

Using the same integral from part A, we can evaluate it as:

Total Distance = (-14/3) meters

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To determine which point is a solution to which equation system, you have to identfy which line corresponds to which equation and the coordinates of each point.

Points

W (≈-7/3,≈4/3)

X (-1,3)

Y (1,1)

Z (≈-1/2,-2)

The symbol ≈ indicates that is an approximate value.

Brown line

Has y-intercept at (0,-3)

And slope

Using points (0,-3) and (-1,-1)

Its equation is y=-2x-3

Blue line

Has y-intercept (0,2)

And slope

Using points (0,2) and (-1,-3)

Its equation is y=-x+2

Red line

Has y-intercept (0,4)

And slope

Using points (0,4) and (-1,-3)

Its equation is y=x+4

Black line

Has y-intercept (0,-1)

And slope

Using points (0,-1) and (1,1)

The equation for this line is y=2x-1

The first equation system is

y=-2x-3

y=2x-1

Corresponds to the intersection between the brown and black lines. The point that is a solution for this system is Z

The second equation system is

y=x+4

y=-x+2

Corresponds to the intersection between the blue and red lines. The point that is a solution for this system is X

The third equation system is

y=-2x-3

y=x+4

Corresponds to the intersection between the brown and red lines. The point that is a solution for this system is W

The fourth equation system is

y=2x-1

y=-x+2

Corresponds to the intersection between the black and blue lines. The point that is a solution for this system is Y

Another way for solving this exercise is by calculating the solution of each system and placing the results in the grid. For example for the first system:

y=-2x-3

y=2x-1

solve for x

And now replace this value in one of the equations

The solution for this system is (-1/2,-2) → If you look at the coordinates determined above, you'll see that these correspond to point Z

Both ways are equally valid to determine which point corresponds to each system.

The simplified expression is 2x⁵.

To simplify the expression \(\left(4x^{9/2}\right)\left(\frac12x^{1/2}\right)\), we can multiply the coefficients and combine the variables with the same base.

Multiplying the coefficients: \(4 \times \frac12 = 2\)

Multiplying the variables with the same base:

\($x^{9/2} \times x^{1/2} = x^{\left(\frac92 + \frac12\right)} = x^{10/2} = x^5$\)

Putting it all together, the simplified expression is \(2x^5\)

Hence the simplified expression is 2x⁵.

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The best approximation of the volume of a cylinder with a radius of 10 mm, and a height of 5 mm using 3.14 for pi is 1,570 cubic millimeters.

The formula for calculating the volume of a cylinder is as follows:

V = πr²h

Where V is the volume, r is the radius of the cylinder, and h is the height of the cylinder.

Substituting the values given in the formula, we have :

V = πr²hV = 3.14 × (10 mm)² × (5 mm)V = 3.14 × 100 mm² × 5 mm

V = 1,570 cubic millimeters.

Therefore, the best approximation of the volume of a cylinder with a radius of 10 mm, and a height of 5 mm using 3.14 for pi is 1,570 cubic millimeters.

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Answer:

equate two simultaneous equations for r and solve