a study of nickels showed that the standard deviation of the weight of nickels is 300 milligrams. A coin counter manufacture wishes to find the 90% confidence interval for the average weight of a nickel. What is the minimum number of nickels he needs to weigh to obtain an average accurate to within 20 milligrams?

This system of equations has infinitely many solutions.

An equation is a mathematical statement that two expressions are equal. It can be written using numbers, symbols, and mathematical operations such as addition, subtraction, multiplication, and division. Equations can also be used to describe relationships between known values, like a line of best fit for data points. Equations are used in many areas of mathematics, such as geometry and calculus, to help solve problems or to describe physical phenomena.

This can be determined by looking at the coefficients of the variables. Since the coefficients of x in each equation are the same and the coefficients of y in each equation are different, this indicates that the equations are not equivalent and therefore, have infinitely many solutions.

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Answer:

4

Step-by-step explanation

for a rectangle you have to lengths and 2 width so you will have to have 2w+2 and then times 4w+3 which should equal 56

Answer:

----------------------------

Total number of frequencies:

Number of frequencies with the outcome of less than 2:

Probability of a number less than 2:

The matching choice is D.

Answer:

[tex]\sf D. \quad \dfrac{12}{60}[/tex]

Step-by-step explanation:

Experimental probability is based on the actual results of an experiment.

Theoretical probability is based on possible outcomes based on assumptions.

Experimental probability

Calculated by dividing the number of times an event happens by the total number of trials in an actual experiment.

[tex]\boxed{\textsf{Experimental Probability} = \dfrac{\textsf{Number of times an event happens}}{\textsf{Total number of trials}}}[/tex]

From inspection of the given table, the actual results (frequency) of landing on a number less than 2 is 12.

The total number of trials is 60.

Therefore:

[tex]\sf \implies P(x < 2)=\dfrac{12}{60}[/tex]

The angle measure used to create each section of the circle graph are (a) 90  (2) 195  (3) 72

The given parameters that will help us to find the angles are:

The measure of the angles are:

1)  number that use train =125/500 * 360 = 90⁰

2) Degree of people airplane is 275/500 *360 = 198⁰

3) Number that use boat = 100/500 * 360 = 72⁰

In conclusion the measurement of the angles for the three means are 90 degrees, 198 degree and 72 degrees respectively

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Using the distributive property, the algebraic expression 15(2 + r) can be rewritten as: 30 + 15r.

To use the distributive property to rewrite an algebraic expression, you need to multiply the value outside the parentheses by each value inside the parentheses.

For example, if you have the expression "a(b + c)", you would use the distributive property to rewrite it as "ab + ac".

15(2 + r) (given)

15 * 2 + 15 * r

30 + 15r

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Therefore , the solution to the given problem of combination comes out to be  1,2,3,4, 5,6,7,8,9 .

Combinations are a method for determining an event overall results where the results' sequence is immaterial. Combinations will be calculated and use the formulae nCr = n! / r! * (n - r)!, were n includes the number of items and r represents the number of things being picked at a time.

Here,

Given: (14) 9,10, 11,12,.., 25

= A group of natural integers between 9 and 25.

(18)

The lowercase letter x follows d and comes before j in the alphabet.

e, f,g, h, I

(22)

the collection of natural numbers below 10.

1,2,3,4, 5,6,7,8,9 .

Therefore, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are the answers to the given combination problem.

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Therefore , the solution to the given problem of triangle comes out to be the length MP is measured at 6 units.

Due to its three vertices and three sections, a component is a polygon. It has a simple geometric form. Triangle ABC refers to a triangle only with points A, B, and C. When components are not collinear, a singular plane and triangle are found. Triangles are regarded as polygons since they have three corners and a right side. The points where a triangle's three sides intersect are known as the triangle's corners. By compounding three triangle angles, one gets 180 degrees.

Here,

Triangle OMN is provided.

Now, OMN and OPQ are comparable. It follows that the side lengths are in proportion to one another. We can write:

=>OP = OM = PQ = MN

=>OM = PQ/MN in 12

=>(OP + PM)/12 = PQ/MN

Considering that -

=>PQ = MP + 2

=>12/(OP plus PM) = (MP plus 2)/MN

=>12MN equals (MP + 2)(OP + PM).

=>12 × 12 = (MP + 2)(MP + 12)

=>2 MP plus 12 MP plus 2 MP plus 24 = 144

=>(MP)² + 14(MP) - 120 = 0

We can write - if MP = x.

=>x² + 14x - 120 = 0

=>(x + 20)(x - 6) = 0

=>(x + 20) = 0 and (x - 6) = 0

x = - 20 and x = 6

There can be no negative lengths, hence x = 6

Consequently, the length MP is measured at 6 units.

Therefore , the solution to the given problem of triangle comes out to be the length MP is measured at 6 units.

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Outputs represent your y - values in coordinate.

Input represent your x - values in coordinate.

A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.

We know that;

A relation is said to be a function if set of inputs having one output each.

Hence, In coordinate (x, y);

All x - values represents inputs and all y - values represent outputs.

Hence, Outputs represent your y - values in coordinate.

And, Input represent your x - values in coordinate.

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Answer:

Step-by-step explanation:

The Answer is 12.5 because...

200/5=40

40x12.5=500

So that means 12.5x40=500

The correct transformation is Horizontal Compression, Left 1 , Up 2.

What is transformation?

An operation that manipulates a polygon or other two-dimensional object on a plane or coordinate system is known as a transformation.

The shape in two dimensions before any alteration is known as a pre-image or inverse image. The shape after transformation is the image.

Given: [tex]f(x)=\sqrt{3x+3} +2[/tex]

The parent function of given function is square root function.

[tex]f(x)=\sqrt{x}[/tex]

Shift 1 unit left

[tex]f(x)=\sqrt{(x+1)}[/tex]

Horizontal Compression

[tex]f(x)=\sqrt{3(x+1)}[/tex]

Vertical up by 2 units

[tex]f(x)=\sqrt{3x+3}+2[/tex]

Hence, the parent function [tex]f(x)=\sqrt{x}[/tex], horizontally shrink by a factor of 3 , shift 1 unit to the left, shift 2 units upwards.

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Question: Given the function,[tex]f(x)=\sqrt{3x+3} +2[/tex], choose the correct transformation(s).

Correct options are C, D. On simplifying, a^(1/n) = r  can be written as n√a = r and a = rⁿ.

The fundamental guidelines and procedures to simplify any algebraic statement are as follows:

By multiplying factors, remove any grouping symbols like brackets and parenthesis.

If the words contain exponents, use the exponent rule to eliminate grouping.

Add or subtract like terms to combine them.

Add the constants together.

Given,

a^(1/n) = r                                      ...........(1)

It can be written as -

n√a = r

secondly,

multiplying power n on both sides of equation (1)

we get,

a = rⁿ

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The given function is continuous over the domain [-3,-2].

If a function f is continuous throughout its whole domain, it is referred to as a continuous function. A point in the domain of a function f at which the function is not continuous is known as the point of discontinuity of the function. is a perpetual function. The only non-zero number in the domain is 2.

Every polynomial function on R and every rational function on its domain are both continuous. Proof. On R, the identity function g(x) = x and the constant function f(x) = 1 are both continuous.

Either a discrete or continuous domain is possible. A discrete function would have x-values that can stand on their own with no surrounding interval.

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Answer:

20) Rhombus | 21) Rhombus | 22) Square

Step-by-step explanation:

20) All sides are congruent, but there is no right <'s, and therefore it is just a Rhombus.

21) A Rhombus has diagonals that bisect each other and are congruent, which is shown in 21.

22) A square is a shape with all sides congruent and at least 1 right angle, which the diagram meets.

Hopefully this helps!

The number of toys based on the information will be 5.

From the information, Edgar works in the shipping department of a toy manufacturer. Toy cars weigh 6 pounds apiece and are shipped in a container that weighs 5 pounds when empty. Toy trucks, which weigh 3 pounds apiece, are shipped in a container weighing 20 pounds.

This will be Illustrated as:

5 + 6t = 20 + 3t

Collect the like terms

6t - 3t = 20 - 5

3t = 15

Divide.

t = 15 / 3

t = 5

The number of toys is 5.

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The value obtained after calculating the first partial product of 26 × 107 is, 214

It is a mathematical technique, by which we do a multiplication operation by doing the sub-parts of the multiplier and then we do separately multiplication, after that we add both the results.

Given numbers,

26×107

Two sub-parts (26) of multiplier

26 = 2×13

First partial multiplier = 2

Second partial multiplier = 13

First partial product = 2×107 =214

Hence, First partial product 214

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Answer:

4.85

Step-by-step explanation:

8.09-3.24+4.85

Answer:

7/4

Step-by-step explanation:

4 1/8=33/8

2 3/8=19/8

-----------------

33/8-19/8=14/8=7/4

On solving the provided question, we can say that we have two quadratic equations; t² +9t + 36 > t² + 11t + 12 => t>12

A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. An equation that is quadratic is a quadratic equation. This indicates that it has at least one word that has to be squared. The formula "ax2 + bx + c = 0" is one of the often used solutions for quadratic equations. where are numerical coefficients or constants a, b, and c. where the variable "X" is unidentified.

here,

we have two quadratic equations

Mall A is modeled by -t² +9t + 36,

Mall B is modeled by - t² + 11t + 12,

t² +9t + 36 > t² + 11t + 12

-2t > -24

t>12

Mall A when t = 3 hours = [tex]3^2 +9*3 + 36 = 9+27+36 = 72[/tex]

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The answer is 10 minutes

The unitary method is a method in which you find the value of a unit and then the value of a required number of units.

Given here: Abrams family had a 30-gallon baby pool that they could fill in just 2 minutes. Thus speed = 30/2

                                                   =15 gallons per day

Thus to fill 150 gallons the time required is 150/15=10 mins

Hence, The answer is 10 minutes

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The coordinate matrix of x relative to an orthonormal basis b in [tex]R^n[/tex] can be found by computing the inner product of x with each basis vector and representing these inner products as the entries of a column vector.

To find the coordinate matrix of x relative to an orthonormal basis b in R^n, we need to express x as a linear combination of the basis vectors in b. This can be done by computing the inner product (dot product) of x with each basis vector and representing these inner products as the entries of a column vector. The resulting vector is the coordinate matrix of x relative to the orthonormal basis b.

For example, let x be a vector in [tex]R^n\\[/tex], b = [tex]{b_1, b_2, ..., b_n}[/tex] be an orthonormal basis in R^n, and let A be the coordinate matrix of x relative to b. Then the entries of A are given by:

A = [tex]( x, b_1 , x, b_2 , ..., x, b_n )^T[/tex] where [tex]x, b_i[/tex] denotes the inner product of x and [tex]b_i[/tex].

It is important to note that the basis b must be orthonormal for the coordinate matrix to have this form, if the basis is not orthonormal, the process will be different.

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Answer:

$203

Step-by-step explanation:

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The number of mechanical pencils Kimberly own are 61.

What is arithmetic?

In general, the term "arithmetic" (which comes from the Greek word "arithmos," "number") refers to the fundamental concepts of number theory, arts of mensuration (measurement), and numerical computation (that is, the processes of addition, subtraction, multiplication, division, raising to powers, and extraction of roots).

Given:

Jacqueline, Kimberly, and Julia collect mechanical pencils.

Kimberly owns two less than three times the number of mechanical pencils Jacqueline owns.

Julia owns three less mechanical pencils than Jacqueline.

Together, the three collectors own a total of 100 mechanical pencils.

We have to find the number of mechanical pencils Kimberly own.

Let the mechanical pencils of Jacqueline is x.

As Kimberly owns two less than three times the number of mechanical pencils Jacqueline owns.

⇒  The mechanical pencils of Kimberly are 3x - 2

As Julia owns three less mechanical pencils than Jacqueline.

⇒  The mechanical pencils of  Julia are x - 3

The three collectors own a total of 100 mechanical pencils.

⇒  x + (3x - 2) + (x - 3) = 100

                         5x - 5 = 100

                              5x = 105

                                x = 21

⇒ Mechanical pencils does Kimberly own are 3(21) - 2 = 63 - 2 = 61.

Hence, the number of mechanical pencils Kimberly own are 61.

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Answer:

The answer is (A) 57

Step-by-step explanation:

[tex]4x^{2} + 3y = 4(3^{2}) + 3(7) \\= 4(9) + 21 \\= 36 + 21 \\= 57[/tex]

Hope this helps!

Answer:

A. 57

Step-by-step explanation:

If x is equal to 3 and y is equal to 7 then the equation should be written like this,

4 x (3)² + 3 x 7

Then solve it

First solve the number in the bracket

(3)² = 9

Then

4 x 9 + 3 x 7

According to BODMAS, we should solve numbers that need to be multiplied

4 x 9=36

3 x 7= 21

Then add those two numbers

36+21

The answer is 57

Hope this helps

The polynomial is x^4 - 8x^3 - 30x^2 + 144x + 405 = 0. The solution is obtained using the concept of bi-quadratic equation.

A 4-degree equation is a bi-quadratic equation.

Sometimes the phrase "bi-quadratic equation" is used as a substitute for the phrase "quartic equation." Such problems variable are straightforward to resolve because they can be reduced to quadratic equations in the variable x=z^2, which can then be solved for x using the quadratic formula and then in terms of the original variables by calculating the square roots.

Here,

We are given two roots of the bi-quadratic equation which are -3 and 7 - 2i.

Now, we will find the other two roots of the bi-quadratic equation by using the conjugates of the given roots.

In order to find the conjugate of complex numbers, we have to change the sign of the imaginary part.

So, we will get the conjugate of 7 - 2i = 7+2i

Thus, all the four roots of the bi-quadratic equation are -3, 7+2i, 7 - 2i and -3.

If two roots of an equation are given as a and b, then we can express the equation as (x-a) (x-b) = 0.

So, using this, we will form the equation with two imaginary roots 7+2i and 7−2i, which is given as:

[x-(7−2i)][x-(7+2i)]=0

⇒[x-7+2i][x-7-2i]=0

⇒[(x-7)+2i][(x-7)−2i]=0

Using the identity (a+b)(a-b)=a^2-b^2 , we get

(x-7)^2-(2i)^2=0

∵i=√-1

⇒(x-7)^2+(√-4)^2=0

⇒(x-7)^2+(-4)=0

⇒(x-7)^2 - 4=0

Now we will form the equation with roots -3 and -3, which is

[x-(-3)][x-(-3)]=0

⇒(x+3)^2=0

Finally, we will now find the product of these two quadratic equations to get the required bi-quadratic equation

⇒[(x-7)^2 - 4] [(x+3)^2]=0

⇒[x^2 + 49 - 14x -4] [x^2 + 9 + 6x]=0

⇒[x^2 + 45 - 14x] [x^2 + 9 + 6x]=0

⇒x^4 + 9x^2 + 6x^3 + 45x^2 + 405 + 270x - 14x^3 - 126x - 84x^2 = 0

⇒x^4 - 8x^3 - 30x^2 + 144x + 405 = 0

Hence, the required polynomial is x^4 - 8x^3 - 30x^2 + 144x + 405 = 0

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The value of expression 254 ÷ 6 is, 42.33.

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

The expression is,

⇒ 254 ÷ 6

Divide the numbers as;

⇒ 254 ÷ 6

⇒ 254 / 6

⇒ 42.33

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Answer: To calculate the percentage decrease in the number of available seats, we can use the following formula:

(original value - new value) / original value * 100

In this case, the original value is 125 (the number of available seats before the reduction) and the new value is 93 (the number of available seats after the reduction). Plugging these values into the formula:

(125 - 93) / 125 * 100 = 32 / 125 * 100 = 0.256 * 100 = 25.6

So, there is a 25.6% decrease in the number of available seats.

Step-by-step explanation:

The given expression is:

(23^20-53^19)/(-9)^9

This is a mathematical expression that involves multiple operations. The first step is to understand the order of operations, or PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction)

Parentheses: The expression does not contain any parentheses, so we can move on to the next step.

Exponents: The first term, 23^20, contains an exponent. The exponent operator (^) has higher precedence than the multiplication operator (), so we will simplify the exponent first. 3^20 is equal to 3 raised to the power of 20, which is equal to 3 * 3 * 3 * ... * 3 (20 times) = 59,049. Therefore, the first term is now 2 * 59,049.

The second term 5*3^19 also contains an exponent, so we simplify it in the same way as the first term. 3^19 is equal to 3 * 3 * 3 * ... * 3 (19 times) = 7,29,043. Therefore, the second term is now 5 * 7,29,043.

Multiplication and Division: After simplifying the exponents, we can see that the expression contains both multiplication and division. Since division has the same precedence as multiplication, we can simplify the expression from left to right.

The first term 2 * 59,049 is the product of 2 and 59,049. Multiplying these two numbers gives us 118,098.

The second term 5 * 7,29,043 is the product of 5 and 7,29,043. Multiplying these two numbers gives us 36,45,215.

The third term is the division of two terms. We have (23^20-53^19) / (-9)^9

Subtraction : Now we have the subtraction of two terms (118,098 - 36,45,215)

Now we have the division of two terms (-35,27,117) / (-9)^9. In this step, we are dividing the subtraction with -9 raised to the power of 9

The final step is to simplify the division. -9^9 is equal to -9 * -9 * -9 * -9 * -9 * -9 * -9 * -9 * -9 = -3486784401.

So the final expression is -35,27,117/-3486784401.

The expression is a very large negative number divided by a very large negative number, which results in a very small positive number.

If almost a billion people on the planet don't have access to clean drinking water. The percent of them that  lived without clean drinking water is 12.82%.

Given data:

Total number of people =  7.8×10^9

Number of people that lived without clean water = 1 billion

Number of people that lived without clean water = 1,000,000,000 = 1 × 10^9

So,

Percentage of people without clean water=  Number of people that lived without clean water  / Total number of people

Percentage of people without clean  water = 1 × 10^9 / 7.8×10^9 × 100

Percentage of people without clean water = 1/ 7.8 × 100

Percentage of people without clean water= 12.82%

Therefore 12.82% people lived without clean water.

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Answer:

a)  See below.

[tex]\textsf{b)} \quad y=940\left(1.0257\right)^{2x}[/tex]

c)  x is the number of years.

d)  y is the account balance in dollars.

e)  $1728.29

Step-by-step explanation:

Interest is compounded semi-annually, so:

Therefore, calculate 1.0257% of the balance every 6 months:

[tex]\begin{array}{|c|c|}\cline{1-2} \vphantom{\dfrac12} \rm Years& \rm Account\;balance\;(\$) \\\cline{1-2} \vphantom{\dfrac12} 0& 940.00\\\cline{1-2} \vphantom{\dfrac12} 0.5& 964.16\\\cline{1-2} \vphantom{\dfrac12} 1& 988.94\\\cline{1-2} \vphantom{\dfrac12} 1.5&1014.35\\\cline{1-2} \vphantom{\dfrac12} 2&1040.42\\\cline{1-2} \vphantom{\dfrac12} 2.5&1067.16\\\cline{1-2} \vphantom{\dfrac12} 3&1094.59\\\cline{1-2} \end{array}[/tex]

An equation that models this situation is:

[tex]\implies y=940\left(1+\dfrac{0.0514}{2}\right)^{2x}[/tex]

[tex]\implies y=940\left(1.0257\right)^{2x}[/tex]

x is the number of years.

y is the account balance in dollars.

To calculate how much will be in the account after 12 years, substitute x = 12 into the equation from part (b):

[tex]\implies y=940\left(1.0257\right)^{2 \times 12}[/tex]

[tex]\implies y=940\left(1.0257\right)^{24}[/tex]

[tex]\implies y=940\left(1.8386054...\right)[/tex]

[tex]\implies y=1728.2890...[/tex]

Therefore, $1728.29 will be in the account after 12 years.