Each student needs stick of clay to do an art project. If 16 students wanted to make this
art project, how many sticks of clay would they need?

Answer: y=7/5x

Step-by-step explanation: use the formula (y2-y1)/(x2-x1) to find the slope. The coordinates are (5,7) and (0,0). (0-7)/(0-5) is 7/5. Slope = 7/5 and since the line passes through the origin the b is 0.

The total number of holes will be (a)15 and (b) 4 when the drilling machine is used whose standard deviation is 0.0028mm.

The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a dataset is in relation to its mean.

The sum of all values divided by the total number of values constitutes a dataset's mean.

The mean of the holes are given as 4.05 mm(\(\mu=4.08\))

The standard deviation is given as 0.0028 mm(\(\rho=0.0028\))

Now we will use the z-score and probability distribution to calculate the frequency of the holes to have diameter between 4.048 and 4.0553.

Here \(Pr(4.048\leq X\leq 4.0053)\) ,so we need to compute the z-values

\(Z_1=\frac{X_1-\mu}{\rho} \\Z_1=\frac{4.048-4.05}{0.0028} \\Z_1=-0.7143\)

Similarly:

\(Z_2=1.8929\)

Therefore from the above statements we can say that

\(Pr(-0.7143\leq X\leq 1.8929)\)

Solving for probability distribution we get

\(Pr(4.048\leq X\leq 4.0053)=0.7333\)

Total number of holes=0.7333 × 20= 14.666..

Therefore the number of holes is 15

Similarly

The z-value corresponding to 4.052 mm is given by 0.71

The z-value corresponding to 4.056 mm is given by:2.14

The probability of the diameter being between 4.052 mm and 4.056 mm is 0.4838 – 0.2611 =0.2227

The number likely to have a diameter between 4.052 mm and 4.056 mm = 0.2227 × 20

= 4.454

= 4, correct to nearest whole number

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Answer:

option C 7½ is correct hope this answer helps you dear! take care

Since these are parallel lines, the angles formed are congruent ( equal).

So, Angle B=A =60°

Correct option: A-60 °

Answer: 75/100

Step-by-step explanation:

the total number of flowers= 25+15+30+20+10

                                             = 100

so probability that the flower is not a rose is= 75/100

Note: i got 75 by subtracting 100 by 25                                          

Answer:

0=4×4−4×4

Step-by-step explanation:

Answer:

\(\boxed{\mathrm{view \: explanation}}\)

Step-by-step explanation:

1 = 4 ÷ 4

2 = (4 + 4) ÷ 4

3 = (4 + 4 + 4) ÷ 4

4 = 4 + 4 - 4

5 = (4 × 4 + 4) ÷ 4

6 = (4 + 4) - (4 ÷ 4) - (4 ÷ 4)

7 = (4 + 4) - (4 ÷ 4)

8 = 4 + 4

9 = (4 + 4) + (4 ÷ 4)

10 = (4 + 4) + (4 ÷ 4) + (4 ÷ 4)

$454.32

given

Step 1

a) let x represent the original price

so, if the original price was reduced by 5/6 to obtain $378.6 we can set an equation:

now, to solve multiply both sides by 6/5

therefore, the original price is

$454.32

I hope this helps you

This is a True statement that both the matrix equation and the augmented matrix translate into the same system of linear equations.

What are Linear equations?

An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation.

A rectangular matrix is a grouping of numbers into rows and columns. Systems of equations can be solved using matrices. But first, we need to understand how to use matrices to represent systems.

An augmented matrix can be used to express a set of equations. Each column in an augmented matrix represents a variable or the constant terms, and each row in an augmented matrix represents one equation in the system. As a result, it is clear that augmented matrices provide a convenient approach to express systems of equations.

Therefore it is true that the solution set of the equation's equation is the same as the solution set of the linear system whose augmented matrix is.

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The fence in dead center is about 399 feet from the third base.

The Pythagorean Theorem states that in the case of a right triangle, the square of the length of the hypotenuse, which is the longest side,  is equals to the sum of the squares of the lengths of the other two sides.

Hence the equation for the theorem is given as follows:

c² = a² + b².

In which:

For the triangle in this problem, we have that:

Hence the distance is obtained as follows:

d² + 90² = 409²

\(d = \sqrt{409^2 - 90^2}\)

d = 399 ft.

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Part (a)

\(v=22(3)^{d/10}\)

Part (b)

We can rewrite the function as \(v=22(3^d)(3^{1/10})\). Thus, the percentage is \(100(1-3^{1/10})=11.6\%\)

A model for the number of views, v, as a function of the number of days, d, since there were 22 views is \(v = 22(3)^{d/10}\) and the views increasing per day by 11.6%.

Exponential growth is a pattern of data that shows greater increases with passing time, creating the curve of an exponential function.

Given that, The total views of an online video are tripling every ten days. Initially there are 22 views of the video, v represents the number of views and d represents days

a) Since the number of views are tripling every ten days, so, the function will be =  \(v = 22(3)^{d/10}\)

b) We have function \(v = 22(3)^{d/10}\)

So, percentage = \(100(1-3^{1/10})\) = 11.6%

Hence, A model for the number of views, v, as a function of the number of days, d, since there were 22 views is \(v = 22(3)^{d/10}\) and the views increasing per day by 11.6%.

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Answer:

(−14.850850 ; 0.565135)

Step-by-step explanation:

Confidence interval :

Xd ± Tcritical * Sd/√n

Population 1 :30 35 23 22 28 39 21

Population 2 : 45 49 15 34 20 49 36

d = -15,-14,8,-12,8,-10,-15

The mean of d, Xd = Σx / n = - 7.14285714

The standard deviation of the difference, Sd = 10.4948967 (using calculator)

Sample size, n = 7

Tcritical at 90%, df = 7 - 1 = 6

Tcritical = 1.943176

Confidence interval :

- 7.14285714 ± 1.943176 * 10.4948967/√7

Confidence interval :

- 7.14285714 ± 7.7079925

(−14.850850 ; 0.565135)

The function is continuous in the domain x ≥ 3/4

Here we have a root function:

f(x) = ⁴√(4x - 3)

This is an even degree root function, so we have problems when the argument is negative.

Then the allowed values (where the function is defined, and thus, continuous) are:

4x - 3 ≥ 0

4x ≥ 3

x ≥ 3/4

There the function is continuous.

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The area of a circle is calculated using the formula:

A = πr^2

Where A is the area and r is the radius of the circle.

In this case, the radius is given as 7. Substituting the value into the formula:

A = π(7)^2

A = π(49)

A = 49π

The exact area of the circle is 49π square units.

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Answer:

8517/1000 or 8.517 = (8 x 1) + (5/10) + (1/100) + (7/1000)

Step-by-step explanation:

first one is an improper fraction and the other is in it's expanded form.

9514 1404 393

Answer:

  x in {-6, -2, 4}

Step-by-step explanation:

The zero product rule tells you that a product will be zero if and only if one of the factors is zero. These binomial factors are zero when x has a value that is opposite the constant of the binomial.

  x +6 = 0   ⇒   x = -6

  x -4 = 0   ⇒   x = 4

  x +2 = 0   ⇒   x = -2

The zeros of the function are the x-values -6, -2, and 4.

The highest height for the daily rainfall were for 5 and 6 inches

Dot plots are used to present data in the form of points or small circles. It is similar to a simplified histogram or bar graph in that the height of the bar made up of points represents the numerical value of each variable. Dot plots are used to represent small amounts of data.

From the given dot plot, we see the number of times for each height of rainfall.

Thus, we see that the highest number of times of rainfall height was from that of 5 and 6 inches.

Thus, we conclude those were the highest heights for the daily rainfall.

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Answer:

area = 6 units²

perimeter = 10.06 units

Step-by-step explanation:

area = 1/2bh

area = 1/2(4)(3) = 6 units²

perimeter = 4.123 + 2.236 + 4.243 = 10.06 units

The percent of the increase, rounded to the nearest tenth of a percent, concerning the sales of boxes of cookies that Molly sold last month and this month, is 11.5%.

The percentage increase can be determined by finding the difference or the amount of increase in sales.

This difference is divided by the previous month's sales and multiplied by 100.

The total number of boxes of cookies Molly's Scout Troop sold last month = 148

The total number sold this month = 165

The increase = 17 (165 - 148)

Percentage increase = 11.5% (17 ÷ 148 x 100)

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I = C₀*i*t

I = 10.000*0,05*5

I = 2.500

C = C₀ + I

C = 10.000 + 2.500

C = 12.500

The option that is not true about polynomial functions is:

Option D. The deg (f ^ 3) = 3m​

For polynomial functions f(x) and g(x), if deg(f) = m * deg(g) = n, then we have the following:

Option A: deg(f + g) = max(m, n)

This is true because we know that the degree of the sum of two polynomials is the maximum of their individual degrees.

Option B: deg(f * g) <= m + n

This is true because we know that the degree of the product of two polynomials is at most the sum of their individual degrees.

Option C: If g is a factor of f, then deg(f) <= m

This is true because If g is a factor of f, it means that f can be divided by g without leaving a remainder. In this case, the degree of f is less than or equal to the degree of g.

D. The deg(f ^ 3) = 3m

This is not true because the degree of the polynomial f raised to the power of 3 is not necessarily equal to 3 times the degree of f. The degree of f^3 will depend on the individual terms and their exponents.

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Answer: A

Step-by-step explanation: Pic is attached. Hope this helps.

For given that L has been defined to refer to a list , the expression whose value is a set containing all the elements of L is

set = { 1,2,3,4}

Lists are used to store multiple items in one variable. Lists are one of Python's four built-in data types used to store collections of data, the other three being tuples, sets and dictionaries, all of different qualities and uses.

A list is a container which holds comma-separated values (items or elements) between square brackets where items or elements need not all have the same type.

#Programme representation

Input:

#Python code

#A list L is initialised

L = [ 3,4,2,1 ]

#set L containing all elements of list L

print(str(set(L)))

Output:

{ 1, 2, 3, 4 }

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Answer: The value of \((g - f)(x)=4 .\)

Step-by-step explanation:

Given functions :  \(f(x) = x + 4\) and \(g(x) = x + 7\)

To find : \((g - f)(x)\)

Difference between two functions: \((u-v)(x)=u(x)-v(x)\)

Then, \((g-f)(x)=g(x)-f(x)\)

\(=(x+7)-(x+4)=x+7-x-4\\\\=7-4=3\)

Hence, the value of \((g - f)(x)=4 .\)

Answer:the answer is B

Step-by-step explanation:

Answer:

-74 your welcome

Step-by-step explanation:

Answer:

-b-6

Step-by-step explanation:

4(1-2b)+7b-10 multiply inside the parenthesis with 4

4 - 8b + 7b - 10 now add like terms

-b - 6

Answer:

-b-6

Step-by-step explanation:

\(4(1-2b)+7b-10\\\)

Expand

\(4\left(1-2b\right):\quad 4-8b\)

\(=4-8b+7b-10\)

Simplify

\(\mathrm{Simplify}\:4-8b+7b-10:\\\\\quad -b-6\)

Answer:

What are you subtracting 25 from?

Step-by-step explanation:

a)

0.00000000007

b)

0.00000001

Answer:

sept one

Step-by-step explanation:

Answer:

\(x=12.07\)

Step-by-step explanation:

From the question we are told that:

Mean \(\=x =12cm\)

Standard deviation \(\sigma=0.04\)

Significance level \(\alpha=5\%=0.05\)

Therefore

Confidence level \(95\%=0.95\)

From table \(P(z<1.645)=0.95\)

Generally the equation for Z-score is mathematically given by

\(z=\frac{x-\mu}{\sigma}\)

\(x=z\sigma+\mu\)

\(x=1.645*0.04+12\)

\(x=12.07\)