A variable needs to be eliminated to solve the system of equations below. Choose the correct first step. -7x - 10y = -83 4x - 10y = 16 O Subtract to eliminate y. Subtract to eliminate x. Add to eliminate x. Add to eliminate y.

The expected value of each warranty sold is the amount of $15.

A written guarantee of a product's integrity and the maker's duty for the repair or replacement of damaged parts.

As per the question, the required solution would be as:

The expected cost of a failed product without a warranty is :

= $100 x (6/100)

= $100 x 0.006

Apply the multiplication operation,

= $0.6.

The expected cost of a failed product with a warranty is :

= $100 x 0.006 + $15 = $15.6.

So the expected value of each warranty sold is :

= $15.6 - $0.6

Apply the subtraction operation, we get

= $15.

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The required cost of the extended warranty is given as $115, as pe the given condition.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

Here,
The original warranty period but within 2 years of the purchase, with a replacement cost of $100.  They offer a 2-year extended warranty for $15,
Expected value = 100 + 15 = $115

Thus, the required cost of the extended warranty is given as $115, as per the given condition.

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The point slope form of the equation is y-5=4(x-3).

What is point slope form of the equation?

The slope of a straight line and a point on the line are both components of the point-slope form. The equations of infinite lines with a specified slope can be written, however when we specify that the line passes through a certain point, we obtain a singular straight line. In order to calculate the equation of a straight line in the point-slope form, only the line's slope and a point on it are needed.

Here the given point [tex](x_1,y_1)=(3,5)[/tex] and slope m=4 then using equation of line formula,

=> [tex]y-y_1=m(x-x_1)[/tex]

=> y-5 =4(x-3)

Hence the point slope form of the equation is y-5=4(x-3).

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Answer:

The demand curve is shown below, with the equation P = 50 - 1Qp. The supply curve is shown below, with the equation P = 40 + 1Qs. The point at the market equilibrium is shown with an asterisk, where the two curves intersect.

Demand Curve: 60- 50- * 40- 30- 20- 10- Price 0 2.5 5 10 7.5 Quantity 12.5 15 Q ON

Supply Curve: 60- 50- 40- * 30- 20- 10- Price 0 2.5 5 10 7.5 Quantity 12.5 15 Q ON

Answer:

Step-by-step explanation:

P(A or B) = P(A) + P(B) - P(A and B) = 0.6 + 0.5 - 0.3 = 0.8.

The incorrect statement is that You can solve for the unknown side in any triangle, if you know the lengths of the other two sides, by using the Pythagorean theorem.

Pythagoras theorem states that for a right angled triangle, the square of the hypotenuse is the sum of the squares of base and altitude.

Pythagoras theorem is only applied for right angled triangles.

There is hypotenuse which is the longest side for only right angled triangles. So we cannot find the length of the third side of any triangle using the Pythagorean theorem.

Hence the statement that you can solve for any triangle's unknown side using the Pythagorean theorem is incorrect.

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Answer: Here are the evaluations of the expression 46 + (-2k) for the given values of k:

For k = 3: 46 + (-2 * 3) = 46 - 6 = 40

For k = 23: 46 + (-2 * 23) = 46 - 46 = 0

For k = -2: 46 + (-2 * -2) = 46 + 4 = 50

So, the evaluated expressions are 40, 0, and 50 respectively.

Step-by-step explanation:

Answer:

Inverse

Step-by-step explanation:

The impulse on an object is equal to the change in momentum of the object. In this case, the ball's initial momentum is 10 kg * 15 m/s = 150 kg m/s. After the collision, the ball's final momentum is -10 kg * 23 m/s = -230 kg m/s.

The change in momentum of the ball is: -230 kg m/s - 150 kg m/s = -80 kg m/s.

So, the impulse on the ball is -80 kg m/s.

The fourth term a₄ of the sequence is 15

The definition of the function is given as

a₁= 6

aₙ = aₙ₋₁ + 3

The above definitions imply that we simply add 3 to the previous term to get the current term

Using the above as a guide,

so, we have the following representation

a₂ = 6 + 3

a₂ = 9

Also, we have

a₃ = 9 + 3

a₃ = 12

Lastly, we have

a₄ = 12 + 3

Evaluate the equation

a₄ = 15

Hence, the value of a₄ is 15

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Complete question

Sequence and series:

If a_1=6 and a_n=a_{n-1}+3, then find the value of a_4

Answer:

below

Step-by-step explanation:

1 is FIRST degree

degree of 2 would be a second degree

Why the length of the third (3) side of a triangle cannot be less than the total of any two (2) of its sides is shown in the diagram: B. by demonstrating that two sides with lengths of 4 and 3 cannot ever come together to form a vertex.

The definition of a triangle is a two-dimensional geometric figure with exactly three (3) sides, three (3) vertices, and three (3) angles. According to the length of their sides, triangles fall into one of the following three (3) categories:

By applying the Triangle Inequality Theorem to this diagram (see attachment), we have:

4 + 12 > 3 (True).

3 + 12 > 4 (True).

4 + 3 > 12 (False).

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The triangle that is produced is a right-angled triangle, as can be seen in the diagram. ∴ Area of a right-angled triangle [tex]=\frac{1}{2} \times$ base $\times[/tex]height

The triangle that is produced is a right-angled triangle, as can be seen in the diagram.

∴ Area of a right-angled triangle [tex]=\frac{1}{2} \times$ base $\times[/tex]height

Additionally, the right-angled triangle's area ($) (0,0),

[tex](\mathrm{x}, 0),(0, \mathrm{y})=$ $\frac{1}{2}|x y|$ sq.units[/tex]

⇒ Area of the right-angled triangle formed by the points

(0,0),(4,0),(0,3) =  [tex]$\frac{1}{2}|4 \times 3|$[/tex]  sq.units

[tex]$=\frac{1}{2} \times(12)[/tex]

= 6 sq.units

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The probability that a defective component will be detected only by the first inspector is 0.19

The probability that a defective component will be detected by exactly one of the two inspectors is 0.38

The probability that all three defective components in a batch escape detection by both inspectors is 0.

It is given that The first inspector detects 81% of all defectives that are present, and the second inspector does likewise.

Therefore P(A)=P(B)=81%=0.81

At least one inspector does not detect a defect on 38% of all defective components.

Therefore, bar P(A∩B)=0.38

As we know:

bar P(A∩B)=1-P(A∩B)=0.38

P(A∩B)=1-0.38=0.62

A defective component will be detected only by the first inspector.

P(A∩barB)=P(A)-P(A∩B)

=0.81-0.62

P(A∩barB)=0.19

The probability that a defective component will be detected only by the first inspector is 0.19

Part (B) A defective component will be detected by exactly one of the two inspectors.

This can be written as: P(A∩barB)+P(barA∩B)

As we know:

P(barA∩B)=P(B)-P(A∩B) and P(A∩bar B)=P(A)-P(A∩B)

Substitute the respective values we get:

P(A∩ barB)+P(bar A∩B)=P(A)+P(B)-2P(A∩B)

=0.81+0.81-2(0.62)

=1.62-1.24

P(A∩ barB)+P(bar A∩B)=0.38

The probability that a defective component will be detected by exactly one of the two inspectors is 0.38

Part (C) All three defective components in a batch escape detection by both inspectors

This can be written as: P(bar A∪ bar B)-P(bar A∩B)-P(A∩ barB)

As we know bar P(A∩B)=P(bar A∪ bar B)=0.38

From part (B): P(bar A∩B)+P(A∩bar B)=0.38

This can be written as:

P(bar A∪ bar B)-P(bar A∩B)-P(A∩bar B)=0.38-0.38=0

The probability that all three defective components in a batch escape detection by both inspectors is 0

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The factor of [tex]6x^{2}y+8-30y-40[/tex] is 2 ( [tex]3x^{2}y-15y-20[/tex] ).

The factor is a number or quantity by which a given number, quantity, or expression is multiplied to produce another number, quantity, or expression. Factors are usually whole numbers, but they can also be expressions or fractions. Factors are used to simplify or solve equations and expressions. Factors can also be used to determine the greatest common factor (GCF) of two or more numbers or expressions.

The first step is to factor out the greatest common factor (GCF), which in this case is 2. The GCF of [tex]6x^{2}y+8-30y-40[/tex] is 2. Once the GCF is factored out, the expression can be written as 2([tex]3x^{2}y-15y-20[/tex]). Finally, the remaining factors can be combined to get the final factor of 2([tex]3x^{2}y-15y-20[/tex]).

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Step-by-step explanation:

A whole can be divided into many parts and the number of parts will depend on the unit of measurement we use to divide it.

A whole can be divided into fifty equal parts, each of which is called a "fiftieth." So, one whole would be equal to 50 fiftieths.

1 whole = 50 fiftieths

Alternatively, we can say that one fiftieth is equal to 1/50th of a whole. This can be represented as a decimal or a fraction.

1 fiftieth = 1/50th of a whole = 0.02 (decimal)

Answer:

4.2 yrs hope this helped. :)

Step-by-step explanation:

1.1. Given any negative real number s, the cube root of s is negative.

1.2. For any real number s, if s is negative, then the cube root of s is negative.

1.3. If a real number s is negative, then the cube root of s is negative.

The cube root of a real number can be either positive or negative, depending upon the sign of the original number. If the original number is positive, then the cube root can be either positive or negative.

If the original number is negative, then the cube root must and should be negative. This is because multiplying any negative number by itself three times will result in a negative number.

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Given the L-shaped line

where p 1 = ( 0, 2, 2 )

L → Р = Ро + tυwhere p = ( x, y, z ) and p 0 = ( 1, 1, 0 ) and v = ( 1, 2, 2 )

The components p 1 and L constitute a plane with the normal vector n given by

→ \sn \s= \sλ \s1 \s( \sp \s0 \s− \sp \s1 \s)

when R = 1

L 1 is the desired line and is orthogonal to L, so

L 1 p = p 1 + t 1 v 1 = p 1 + t 1 v 1 where

2 v n with 2 R v 1 = 2 v n with 2 R

It is more advantageous to parameterize relations or implicit equations since they become explicit functions once parameterized.

A circle, for example, may be defined as x 2 + y 2 = r 2. When a relation passes the vertical line test, you know it is a function; a circle does not.

When you try to define the circle directly, you get: y = r 2 x 2. Again, this is not a function; it is the combination of two functions.

When we parameterize a circle, we get: x = r cos t

y \s= \sr \ssin \st

t \s∈ \sR

Both x and y are explicit functions that may be plotted, integrated, or differentiated as needed.

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The parametric equation of the plane is x = 11/6 t, y = -5/2t, z = 1 1/2 t.

(x, y, z) = (0, 2, 2) + t(i - j +2 k)

A plane that is parallel to this line will have the general equation:

x - y + 2z = c

We make it contain the point by substituting in the point and solving for c:

0 + 2 +2(2) = 4

c = 4

The plane x - y + 2z = 4 contains the point (0, 1, 2) and is perpendicular to the line.

To find the point where the line intersects the plane, substitute the parametric equations of the line into the equation of the plane:

x - y + 2z = 4

(1 + t) − (2 − t) + 2(2t) = 4

1+t-2+t+ 4t = 4

6t = 5

t = 5/6

x = 11/6, y = 7/6, z=5/3

The line intersects the plane at the point (11/6, 7/6, 5/3)

The vector, v, from the given point to the intersection point

v = (11/6 - 0)i + (7/6 - 2)j + (5/3 - 2)k

v = 11/6 i -5/2 j - 1/2 k

The vector equation of the line is:

(x, y, z) = (0, 2, 2) + t (11/6 i -5/2 j - 1/2 k)

The parametric equations are:

x = 11/6 t,

y = -5/2t,

z = 1 1/2 t

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Maximum value: 9, located at point (-3, 9).

Minimum value: -5/3, located at point (1, -5/3).

[tex]y=\frac{1}{3}x^{3} +x^{2} -3x[/tex]

Check attached images 1 and 2.

[tex]\frac{d}{dx} =y'\\ \\y'=(3*\frac{1}{3})x^{3-1} +2*x^{2-1} -(1*3)x^{1-1} \\ \\y'=x^{2} +2x-3[/tex]

Use the quadratic formula.

Check attached image 3.

a = 1

b = 2

c = -3

[tex]x_{1} =\frac{-(2)+\sqrt{(2)^{2}-4(1)(-3) } }{2(1)} =1\\ \\x_{2} =\frac{-(2)-\sqrt{(2)^{2}-4(1)(-3) } }{2(1)} =-3[/tex]

Quick analysis. This results tell us that the minimun and maximum points different that infinity of the original function ([tex]y=\frac{1}{3}x^{3} +x^{2} -3x[/tex]) are located in points x = 1 and x = -3. Now, we need to discover who's the maximum point and who's the minimum. For this, evaluate both point in the original function.

[tex]y=\frac{1}{3}x^{3} +x^{2} -3x\\ \\f(x)=\frac{1}{3}x^{3} +x^{2} -3x\\ \\f(1)=\frac{1}{3}(1)^{3} +(1)^{2} -3(1)\\\\ =\frac{1}{3}+1-3 \\\\ =\frac{1}{3} +\frac{3}{3}-\frac{9}{3} \\ \\=\frac{1+3-9}{3} \\ \\=-\frac{5}{3}[/tex]

[tex]f(-3)=\frac{1}{3}(-3)^{3} +(-3)^{2} -3(-3)\\ \\=\frac{1}{3}(-27) +(9)-(-9)\\ \\=\frac{-27}{3} +9+9\\ \\=-9+9+9\\ \\=9[/tex]

Maximum value: 9, located at point (-3, 9).

Minimum value: -5/3, located at point (1, -5/3).

Check out the graph (attached image 4) to better understand the method used for this solution.

Note. See that the "x" coordinates where the function has maximum and minimum points are the exact same "x" coordinates where the derivative touches the "y" axis, that's why we calculated the roots of the derivative and then evaluated in the original function.

Answer:

A train traveling at a constant speed of 105 miles per hour covers a distance of 315 miles in 3 hours. To find the distance in feet, we need to convert miles to feet:

315 miles * 5,280 feet/mile = 1,654,400 feet

So, in 3 seconds, the train travels approximately:

1,654,400 feet / (60 seconds/minute * 60 minutes/hour) = 9,072 feet

Therefore, in 3 seconds, the train traveling at a constant speed of 105 miles per hour travels approximately 9,072 feet.

Answer:

To convert miles per hour to feet per second, multiply the speed in mph by 5280/3600 = 1.46667.

105 mph * 1.46667 ft/s = 153.333 ft/s

To find the distance travelled in 3 seconds, multiply the speed by time:

153.333 ft/s * 3 s = 315 ft

Answer:

30.39 and 10.26 pounds.

Step-by-step explanation:

Step 1 of 2: if the variables x (for 41% alloy) and y (for 54% alloy), then

Step 1 of 2: it is possible to make up the system of two equations:

[tex]\left \{ {{x+y=0.45*40} \atop {0.41x+0.54y=0.45(x+y)}} \right. < = > \ \left \{ {{y=\frac{72}{13} } \atop {x=\frac{162}{13}}} \right.[/tex]

then the mass of the alloy containing 41% of coper is 162/13:0.41≈30.39

the mass of the alloy containing 54% of copper is 72/13:0.54=10.26.

Solving the provided question we can say that the  quadratic equation is  [tex]x^2+4x-21[/tex] answer is x = -5 and 1

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.

the  quadratic equation is

[tex]x^2+4x-21[/tex]

answer is x = -5 and 1

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The equation of line that is tangent to the function f is y = 8x - 6 and

y = 8x + 10.

Let's start with the generic equation of a line:

y = ax + b

This line must be parallel to the line 8x - y + 5 = 0, and it must have the same slope.

The slope of the line 8x - y + 5 = 0 is 8, so our line has a = 8 :

y = 8x + b

Now we must determine the b values that make this line tangent to the function f(x) = 2x².

First, compute the derivative of f(x) in relation to x:

4x = df(x) / dx

For any value of x, this derivative is the slope of the tangent line to the function. We require a slope of 8, so:

4x = 8

x = 8/4

x = ±2

To calculate the y-values, we have:

f(1) = 2 x 1² = 2

f(-1) = 2 x (-1)² = 2

Using the points (1,2) and (-1,2) from our parallel line, we get:

2 = 8 x 1 + b is the first line using (1,2).

b = -6

(-1,2) is used in the second line: 2 = 8 x -1 + b

b = 10

The value of b represents the line's y-intercept, so the line with a smaller y-intercept is y = 8x -6, and the line with a larger y-intercept is y = 8x + 10.

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Therefore , the solution of the given problem of angles comes out to be 41.92 angles is the correct option.

In Euclidean space, an angle is indeed a construction comprised of two beams that split at the apex & vertex, which are located in the middle of the angle. The side of loops are the name given to these rays. A combination of two rays may result in an angle that is within the planes in that they are located. Two planes can be combined to form an angle as well. They are referred to as dihedral angles. Two line rays with end points can be arranged in a variety of ways to create styles in two dimensions.

Here,

Given :

=>  speed = 35 feet per second

=> time = 0.8 second

=> height = 9 feet

Distance covered slantly = 0.8 * 35 = 28 feet

=> Sin x = 9/28

=> x =  Sin⁻¹(9/28)

=> x = 41.92

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Answer:

x = 15

Step-by-step explanation:

30 + 4x = 90   These angles are complementary which means that they add to 90.  Subtract 30 from both sides

30 - 30 + 4x = 90 - 30

4x = 60   Divide both sides by 4

x = 15

The required number word that is one more than fourteen is "fifteen."

A number system is described as a technique of composing to represent digits. It is the mathematical inscription for describing the numbers of a given set by using numbers or other characters in a uniform method. It delivers a special presentation of every digit and describes the arithmetic structure.

Here,
In the number system when we add 1 to the number 14, what we get is 15 in words it is fifteen
So,
one + fourteen = fifteen

Thus, the required number word that is one more than fourteen is "fifteen."

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As per the standard deviation, the probability of 8≤ X < 11 is 0.1429.

A random variable X is a mathematical representation of the possible values that a random process or experiment can take on. X has a normal distribution, meaning that its distribution follows a bell-shaped curve.

The standard deviation measures how spread out the values of X are around the mean.

If X has a mean of μ and a standard deviation of 2, then 68% of the values of X will fall within one standard deviation of the mean.

This means that about 68% of the values of X will fall between μ-2 and μ+2.

To find the probability that X falls between 8 and 11, we need to use the cumulative distribution function (CDF).  

Using the standard normal distribution table, we find that P(X < 8) = 0.8413 and P(X < 11) = 0.9842.

Thus, the probability that 8≤ X < 11 is

=> 0.9842 - 0.8413 = 0.1429,

which rounded off to the 4th decimal place is 0.1429.

Complete Question:

Random variable X has a normal distribution with mean μ and standard deviation 2. The pdf f(x) of X satisfies the following conditions: (A) f(6) > f(16), (B) f(1) < f(17). When u is an integer, what is P(8≤ X < 11) (round off to the 4th decimal place)?

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Answer:

5 5/8

Step-by-step explanation:

2 2/3=8/3

8/3x=15

x=15*3/8

x=5 5/8

Answer:

Step-by-step explanation:

67267642qwu62we2q[tex]x^{2} \alpha we2qe\pi qeqe\beta \beta \left \{ {{y=2} \atop {x=2}} \right. \int\limits^a_b {x} \, dx x_{123} \alpha \pi \\ \\ \\ \\ \neq x^{2} \alpha \sqrt[n]{x} \sqrt[n]{x} x^{2}[/tex]e5427856418548248e654815