This is one question in four parts, please answer with clear
working out and explanation.
I would like to learn how to solve.
Thank you
An expert determines the average time that it takes to drill through a metal plate. The standard deviation is known σ = 40 seconds and the drill times are normally distributed. The sample size is n =

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. This means that if we have the lengths of two sides of a right triangle, we can use the Pythagorean Theorem to determine whether the third side is also a side of the triangle.

For example, if we have a triangle with sides of lengths 3 and 4, we can use the theorem to check if the third side is a right triangle:

c^2 = a^2 + b^2

c^2 = 3^2 + 4^2

c^2 = 9 + 16

c^2 = 25

c = 5

Since the square root of 25 is 5, and the length of the hypotenuse is the third side, this triangle has sides of lengths 3, 4, and 5, which are the lengths of a Pythagorean triple.

In summary, if we have the lengths of two sides of a right triangle, we can use the Pythagorean Theorem to determine whether the third side is also a side of the triangle, by checking whether the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides.

To learn more about Pythagorean theorem click here: brainly.com/question/14930619

#SPJ11

Answer:

False

Step-by-step explanation:

-(-21) is positive 21 since there are 2 negative signs, and -21 is negative, therefore they are not the same.

Hope this helps!

Answer:

False. It is equal to 21.

Step-by-step explanation:

-(21) would equal -21

However,

- (- 21) equals 21

The two negatives "cancel" each other out.

Answer: False. It is equal to 21.

Answer:

y=2/7x-4

Step-by-step explanation:

Write in Slope intercept form

y=mx+b

m = slope

b = y intercept

x = x intercept

y = (0,-4)

So,

y = 2/7x+(-4)   substitute

y = 2/7x-4

Answer:

Step-by-step explanation:

1x=67

Answer:

not co linear

Step-by-step explanation:

co linear means on the same straight line. CG is on one line. HG is on another. The might be at right angles,, but they are not colinear.

The polynomial function \(\(f(x) = 2(x^2+3)(x+1)^2\)\) has zeros at -3 with multiplicity 1, and -1 with multiplicity 2. The graph of the function crosses the x-axis at -3 and -1.

To find the zeros and their multiplicities, we set \(\(f(x)\)\) equal to zero and solve for \(\(x\).\)

Setting \(\(f(x) = 0\),\) we have:

\(\[2(x^2+3)(x+1)^2 = 0\]\)

Since the product of two factors is zero, at least one of the factors must be zero. Thus, we solve for \(\(x\)\) in each factor separately:

1. \(\(x^2 + 3 = 0\):\)

  This equation does not have real solutions since the square of a real number is always non-negative. Therefore, this factor does not contribute any real zeros.

2. \(\(x + 1 = 0\):\)

  Solving for \(\(x\), we find \(x = -1\).\) This gives us a zero at -1 with multiplicity 1.

Since the factor \(\((x+1)^2\)\) is squared, the zero -1 has a multiplicity of 2.

Therefore, the zeros for the polynomial function are -3 with multiplicity 1 and -1 with multiplicity 2. The graph of the function crosses the x-axis at both zeros.

To learn more about polynomial function click here: brainly.com/question/29054660

#SPJ11

For the last problem, the equation is x + 1/x = y (let y be the sum).

This is a quadratic equation that can't be solved without a specific value for y.

For the first problem, let the smaller integer be (x-2) and the larger be x. From the equation (x-2)² + x² = 394, solving for x yields

x=14 and x-2=12.

For the second problem, let the fraction be (x+5)/x.

After adding 3 to both the numerator and denominator, the fraction becomes (x+8)/(x+3).

As given, (x+8)/(x+3)=1, solving for x yields x=5, making the original fraction 10/5 or 2.

For the last problem, the equation is x + 1/x = y (let y be the sum).

This is a quadratic equation that can't be solved without a specific value for y.

Read more about quadratic equation here:

https://brainly.com/question/1214333

#SPJ1

Answer:

2/3

Step-by-step explanation:

If the denominators (bottom numbers) of the fraction are the same, just add the numerators (top numbers) together.

Answer:

percentage of lightbulb replacement requests =  34.15 %

Step-by-step explanation:

According to Empirical Rule

interval                                                          %

μ  ±  σ            55  ±  4     ( 51 ; 59 )              68.3

As the question is a percentage between    55  and  51

or  between  51   and  μ  -  σ    by symmetry    is  68.3/2

% of lightbulb replacement requests =  34.15 %

9514 1404 393

Answer:

  y = 2x -6

Step-by-step explanation:

One form you can use for this purpose is ...

  (x2 -x1)(y -y1) = (y2 -y1)(x -x1)

Filling in the given point values, this is ...

  (0 -4)(y -2) = (-6 -2)(x -4)

  -4y +8 = -8x +32

Generally, we like the equation to have coefficients with no common factors. All of these coefficients can be divided by -4.

  y -2 = 2x -8

This can be rearranged to any form you may like--or left as is.

  y = 2x -6 . . . . . slope-intercept form

Answer:

2x^2 - 12*x/2= Area For Shaded Region

Step-by-step explanation:

This works because you find tha area of both and subtract the shaded area by the unshaded area

Answer: Expression for the area of shades region of the figure = 2\(x^{2}\) - 6x

Step-by-step explanation: Area of shaded region = Area of big rectangle - Area of small rectangle

Area of rectangle = length.breadth

Area of big rectangle = 2x.x                                  { . means multiply}

                                     = 2\(x^{2}\)

Area of small rectangle = 12.(x/2)

                                         =6x

∴ Area of shaded region = 2\(x^{2}\) - 6x

To learn more about area of rectangle,

https://brainly.com/question/2607596

Answer:

(3x^2 + 5x +3) (x + 5)

Answer:

d

Step-by-step explanation:

Answer:

\(122+154i\), D

Step-by-step explanation:

\(\mathrm{Apply\:complex\:arithmetic\:rule}:\quad \left(a+bi\right)\left(c+di\right)=\left(ac-bd\right)+\left(ad+bc\right)i\)

\(a=14,\:b=-2,\:c=7,\:d=12\)

\(=\left(14\cdot \:7-\left(-2\right)\cdot \:12\right)+\left(14\cdot \:12+\left(-2\right)\cdot \:7\right)i\)

\(=122+154i\)

The second-order partial derivatives of \(\(f(x, y) = x^2 + y - e^x + y^2\)\)are:

\(\(\frac{{\partial^2 f}}{{\partial x^2}} = 2 - e^x\), \(\frac{{\partial^2 f}}{{\partial y^2}} = 2\),\(\frac{{\partial^2 f}}{{\partial x \partial y}} = 0\),\(\frac{{\partial^2 f}}{{\partial y \partial x}} = 0\)\) . The value of \(\(w(x, y) = x^2 - y^2 + 10x\)\) at \(\(t = \frac{1}{2}\pi\)\) is -1. The value of \(\(\frac{{dw}}{{dt}}\)\)at \(\(t = \frac{1}{2}\pi\)\) is -10.

The second-order partial derivatives of the function f(x, y) = x² + y - eˣ+ y² are as follows:

The second partial derivative with respect to x, denoted by (∂²f)/(∂x²), evaluates to 2 - eˣ. This derivative represents the rate of change of the rate of change of f with respect to x.

The second partial derivative with respect to y, (∂²f)/(∂y²), simplifies to 2. It represents the rate of change of the rate of change of f with respect to y. The mixed partial derivatives, (∂²f)/(∂x∂y) and (∂²f)/(∂y∂x), both evaluate to 0. This indicates that the order of differentiation does not affect the result, implying symmetry in the mixed partial derivatives.

To evaluate the function \(w(x, y) = x^2 - y^2 + 10x\) at t = 1/2π, we substitute x = cos(t) and y = sin(t). Substituting these values into the expression for w yields w(cos(t), \(sin(t)) = cos^2(t) - sin^2(t) + 10cos(t)\). Plugging in t = 1/2π, we find w(0, 1) = -1.

Finally, to find dw/dt at t = 1/2π, we differentiate w with respect to t and substitute t = 1/2π. By taking the derivative, we obtain dw/dt = -2sin(t)cos(t) - 2sin(t)cos(t) - 10sin(t). Substituting t = 1/2π gives dw/dt|t=1/2π = -10.

Learn more about derivative here: https://brainly.com/question/32963989

#SPJ11

Answer:

Step-by-step explanation:

If you divide the figure into two parts by extending the 4 in side, you get a right triangle and a rectangle.

Area of rectangle:

Area of triangle:

Total area is:

Area of the rectangle

Area of triangle

Total

The estimated internal dimension of the skull (d) should be between 47.69 cubic centimeters and 55.38 cubic centimeters for most Chihuahuas.

we'll first isolate the variable "d" by performing some algebraic operations.

15 ≤ 1.04d - 34.6 ≤ 23

Add 34.6 to all parts of the inequality:

15 + 34.6 ≤ 1.04d - 34.6 + 34.6 ≤ 23 + 34.6

49.6 ≤ 1.04d ≤ 57.6

Now, divide all parts of the inequality by 1.04 (the coefficient of "d"):

49.6 ÷ 1.04 ≤ 1.04d ÷ 1.04 ≤ 57.6 ÷ 1.04

47.69 ≤ d ≤ 55.38

So, the estimated internal dimension of the skull (d) should be between 47.69 cubic centimeters and 55.38 cubic centimeters for most Chihuahuas.

learn more about  variable here:

https://brainly.com/question/29583350

#SPJ11

The compound inequality, 15 ≤ 1.04d – 34.6 ≤ 23, relates the estimated shoulder height (in centimeters) of a dog to the internal dimension of the skull, d (in cubic centimeters).

The compound inequality 15 ≤ 1.04d – 34.6 ≤ 23 represents the range of values for the internal dimension of the skull (d) that correspond to the estimated shoulder height of a dog falling between 15 and 23 centimeters.

To interpret the compound inequality, we can solve it step by step. Adding 34.6 to all three parts of the inequality, we get 49.6 ≤ 1.04d ≤ 57.6. Then, dividing all three parts by 1.04, we have 47.69 ≤ d ≤ 55.38.

This means that the internal dimension of the skull (d) should fall within the range of 47.69 to 55.38 cubic centimeters in order for the estimated shoulder height of the dog to be between 15 and 23 centimeters. Any value of d within this range would satisfy the inequality and correspond to the specified shoulder height range for most chihuahuas.

Learn more about compound here:

https://brainly.com/question/29331176

#SPJ11

Answer:

206 and 109

Step-by-step explanation:

400/2 = 200+6 = 206

206/2 = 103+6 = 109

Answer:

The answer, I believe, is 206 and 109.

Step-by-step explanation:

We first have to divide 400 by 2. We get 200. We then have to add 6, which is 206, our first term. Then we repeat the steps. 206 divided by 2 is 103. Adding that to 6 will get us 109, our second term and answer.

Using Green's theorem, we can evaluate the line integral ∮c [y^3 dx - x^3 dy] around the closed curve C given by the equation x^2 + y^2 = 1, parameterized by x = cos(θ) and y = sin(θ) with 0 ≤ θ ≤ 2π.

Green's theorem states that the line integral around a closed curve C of a vector field F can be computed as the double integral of the curl of F over the region R enclosed by C.

First, we need to find the curl of the vector field F = (y^3, -x^3). Taking the partial derivatives of the components with respect to x and y, we obtain:

∂F/∂x = 0 - 3x^2 = -3x^2

∂F/∂y = 3y^2 - 0 = 3y^2

Now, we calculate the double integral of the curl of F over the region R enclosed by the curve C. Since C is a unit circle centered at the origin, the region R is the entire interior of the circle.

Using polar coordinates, we substitute x = cos(θ) and y = sin(θ) into the curl components and multiply by the appropriate Jacobian factor. The integral becomes:

∫∫R (3y^2 - (-3x^2)) dA

∫∫R (3sin^2(θ) + 3cos^2(θ)) dA

∫∫R 3 dA

3 * Area(R)

Since R is the unit circle, its area is π, so the line integral evaluates to:

3 * π

Therefore, the line integral ∮c [y^3 dx - x^3 dy] around the closed curve C is equal to 3π.

To learn more about Green's theorem click here: brainly.com/question/30763441

#SPJ11

To perform polynomial division using Ruffini's method, we need to divide the polynomial P(x) = x^3 - 4x^2 + x + 6 by Q(x) = x + 1. The result of the division will give us the quotient and remainder.

To begin the polynomial division using Ruffini's method, we set up the division table by listing the coefficients of the dividend polynomial P(x) = x^3 - 4x^2 + x + 6 in descending order. Then, we divide the first term by the divisor Q(x) = x + 1.

-1 (as -1 is the root of Q(x) = x + 1) is written on the top row, and the coefficients of P(x) are listed below. The first coefficient, 1, is copied down, and the second coefficient, -4, is multiplied by -1 to get 4. Adding the result, 4, to the next coefficient, 1, gives us 5.

We repeat this process until we reach the last coefficient, 6. The final row of the division table represents the coefficients of the quotient polynomial. In this case, the quotient is x^2 + 5x + 6. The remainder is 0, indicating that the divisor Q(x) is a factor of P(x).Therefore, the result of the polynomial division using Ruffini's method is the quotient Q(x) = x^2 + 5x + 6, with no remainder.

To learn more about polynomial division click here : brainly.com/question/29631184

#SPJ11

The surface whose equation is given. \(rho2(sin2(φ) sin2(θ) + cos2(φ)) = 4\) is a cylinder with radius 2.

The cylinder has two key characteristics, namely surface area and volume, because it is a three-dimensional form. The combined curved surface area of the cylinder and the areas of the two circular bases make up its whole surface area. A cylinder's volume is the term used to describe the three-dimensional space it takes up.

A surface is a representation of a surface in mathematics. Similar to how a curve generalizes a straight line, it is a generalization of a plane but unlike a plane, it may be curved.

A thing or body's top or outer limit. on the water's surface. the surface of the earth. a two-dimensional locus of points that can be flat or curvy (such as the boundary of a three-dimensional region).

The equation of the surface is

\($$\rho^2\left(\sin ^2 \phi+\sin ^2 \theta+\cos ^2 \phi\right)=4\)

equation of a cylindrical surface is \($y^2+z^2=r^2$$$\)

\(\begin{aligned}& y^2=\rho^2 \sin ^2 \phi \sin ^2 \theta \\& \mathrm{y}=\rho \sin \phi \sin \theta\end{aligned}$$\)

and, \($\mathrm{z}=\rho \cos \phi$\)

and, Radius of the cylinder is

\($$r=2 \text {. }$$\)

To learn more about Surface refer to :

brainly.com/question/15836114

#SPJ1

1. The values which the given number sentences true are:

a) 11 b) 5 c) 36

2. After substituting the value of  x we get the value for y as :

a) 6 b) 0 c) 7 d) 15

3. The number sentences are :

a) x ₋ y = 25

b) 5 × p = q ÷ 2

c) 2y ₋ 14 = 6

d) 15 × 4 = 4 ₋ (x₊y)

Given in the first bit we need to find the variables:

a) h ₊ 8 = 19

arrange the constants on one side.

h = 19 ₋ 8

h = 11

b) 2p ₋ 6 = 4

arrange the constants on one side.

2p = 4 ₊ 6

2p = 10

p = 10/2

p = 5

c) 1/3 y = 12

cross multiply.

y = 36

Now in the second exercise we are asked to substitute the x value and get the value of y.

a) y = 3x ₊ 2 if x =8

substitute x value in the equation.

y = 3(8) ₊ 2

y = 24 ₊ 2

y = 26

b) y = 4x ₋ 1 if  x = 1/4

y = 4(1/4) ₋ 1

y = 1 ₋ 1

y = 0

c) y = 0.2x ₊ 5 if x = 10

y = 0.2(10) ₊ 5

y = 2 ₊ 5

y = 7

d) y = 10x ₊ 12 if x = 0.3

y = 10(0.3) ₊ 12

y = 3 ₊ 12

y = 15

In the last third bit we need to frame equations for the given word problems.

a) The difference between two numbers is 25.

let the two numbers be x and y.

x ₋ y = 25.

b) The product of 5 and p is equal to quotient of q and 2.

5 × p = q ÷ 2

c) The difference between 14 and 2y is equal to 6.

2y ₋ 14 = 6

d) The product of 15 and 4 is equal to four less than the sum of x and y.

15 × 4 = 4 ₋ (x₊y)

Learn more about Solving equations here:

brainly.com/question/13729904

#SPJ9

The algebra property used on -9.97 + (4.68 + 13.08)= (-9.97 + 4.68) + (13.08) is; Associative property of addition.

We are given the number expression;

-9.97 + (4.68 + 13.08) = (-9.97 + 4.68) + (13.08)

There are different algebraic properties such as Associative Property, Commutative Property, distributive property, e.t.c

Now, Associative property of addition states that changing the grouping of addends does not change the sum.

For example, (4 + 5) + 6 = 4 + (5 + 6)

Similarly; (7 + 8) + 9= 7 + (8 + 9)

Looking at our question, we see that the only thing that was changed is the grouping of addends and it did not change the sum. This, we conclude that algebra property used is Associative property of addition.

Read more about Algebraic Property at; https://brainly.com/question/11131460

#SPJ1

There are 9 questions on the test.

Let, the number of multiple-choice questions on the test = m

the number of essay questions on the test = s

m + s = 26  .......(1)

So, We are also told that multiple choice is worth 3 points each, so the total number of points for m questions will be 3m.

As essays are worth 8 points each, so the total number of points for s questions will be 8s.

3m + 8s = 123 .......(2)

Now we will use the substitution method to solve a system of linear equations.

From equation (1) we will get,

m = 26 -s

Substituting this value in equation (2) we will get,

3 * (26- s) + 8s =123

78 - 3s + 8s = 123

5s = 123 -78

5s = 45

s = 45/5 = 9

So, there are 9 questions on the test.

Read more about the substitution method:

https://brainly.com/question/22340165

#SPJ4

The complete question is:

Ada’s history teacher wrote a test for the class.

The test is 26 questions long and is worth 123 points.

Ada wrote two equations, where m represents the

number of multiple choice questions on the test, and

s represents the number of essay questions on the test.

m+s= 26

3m + 8s = 123

How many essay questions are on the test?

1. The set of all points in a plane that are the same distance from a given point called Radius. So the option B is correct.

2. A straight line from the center to the circumference of a circle or sphere is Diameter. So the option A is correct.

The set of all points in the plane that are a fixed distance (the radius) away from a fixed point is referred to as a circle (the center).

Radius is the name for any distance that connects a point on a circle to its center. Any two radii have the same length when compared to the definition of a circle. Take note of the fact that the term "radius" is being used to describe both these intervals and their typical length.

The term "chord" refers to the space that connects two points on a circle.

The term "diameter" refers to a chord that runs through the center. Since a diameter is made up of two radii that are connected at their ends, each diameter has a length that is twice as long as its radius.

To learn more about circle link is here

brainly.com/question/15424530

#SPJ4

The complete question is:

1. The set of all points in a plane that are the same distance from a given point called

1. Center

2. Radius

C. Surface area

D. Circumference

2. A straight line from the center to the circumference of a circle or sphere is

A. Diameter

B. Radius

C. Surface area

D. Circumference

Answer:

k is the option that makes sense

Answer:

I think the answer is continuous hope this helps

Step-by-step explanation:

Also got subscribe to my YT channel BlxeVxbes

Answer:

14

Step-by-step explanation:

A fully loaded truck weighs 10 3/5 tons

After unloading the truck weighed 3 2/3 tons

Therefore the weight of the load can be calculated as follows

= 10 3/5 - 3 2/3

= 53/5 - 11/3

= 265-55/15

= 210/15

= 14

Hence the weight of the load 14

In this question, we are given different arithmetic series and asked to find their sums. The arithmetic series are given in different forms, such as a series of numbers or a series of square roots. We need to use the formulas for the sum of an arithmetic series to find the respective sums.

a) For the series 6 + 14 + 22 + ..., we can see that the first term is 6 and the common difference is 8. We can use the formula for the sum of an arithmetic series, Sn = (n/2)(2a + (n-1)d), where n is the number of terms, a is the first term, and d is the common difference. Substituting the values, we get S15 = (15/2)(2(6) + (15-1)(8)) = 15(12 + 14(8)) = 15(12 + 112) = 15(124) = 1860.

b) For the series √2 + √8 + √18 + ..., we observe that the terms are square roots of numbers. We need to simplify the expression and determine the common difference to find the formula for the nth term. Once we have the formula, we can use the formula for the sum of an arithmetic series to find the sum. The calculation process will be explained in more detail.

c) For the series -40 - 33 - 26 - ..., we can see that the first term is -40 and the common difference is 7. Using the formula for the sum of an arithmetic series, Sn = (n/2)(2a + (n-1)d), we can substitute the values to find the sum.

d) For the series 74 + 63 + 52 + ..., we can observe that the first term is 74 and the common difference is -11. We can use the formula for the sum of an arithmetic series to find the sum.

e) The series is not provided, so it cannot be calculated.

In the explanation paragraph, we will provide the step-by-step calculations for each series to find their sums.

Learn more about arithmetic here:

https://brainly.com/question/16415816

#SPJ11